• Syllabus

Topic 3 - Logic, sets and probability

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Sub sections and their related questions

3.1

• 14N.1.sl.TZ0.5a: Write down in words, the inverse of \(p \Rightarrow q\).
• 14N.1.sl.TZ0.5b: Complete the following truth table.
• 15M.1.sl.TZ2.5a: Complete the following truth table.
• 15M.1.sl.TZ2.11b: Write down in symbolic form the compound statement \(r:\) If \(x\) is a multiple of \(12\), then...
• 15M.2.sl.TZ1.2a: Write the following argument in symbolic form. “If the land has been purchased and the building...
• 15M.2.sl.TZ1.2b: In your answer booklet, copy and complete a truth table for the argument in part (a). Begin your...
• 15M.2.sl.TZ1.2c: Use your truth table to determine whether the argument in part (a) is valid. Give a reason for...
• 16M.1.sl.TZ1.5a: Consider the following statements \(z\,:\,x\) is an integer\(q\,:\,x\) is a rational...
• 16M.1.sl.TZ1.5b: Write the following argument in symbolic form:“If \(x\) is a real number and \(x\) is not a...
• 16M.1.sl.TZ1.5c: Phoebe states that the argument in part (b) can be shown to be valid, without the need of a truth...
• 16N.1.sl.TZ0.5a: Write down in words the compound proposition
• 16N.1.sl.TZ0.5b: Complete the following truth table.
• 16N.1.sl.TZ0.5c: On a morning when Sandi does not get up before eight o’clock, use your truth table to determine...
• 16M.1.sl.TZ2.4a: Consider the following propositions: \(p:\) The lesson is cancelled \(q:\) The teacher is...
• 16M.1.sl.TZ2.4b: Complete the following truth table.
• 16M.1.sl.TZ2.4c: Hence, justify why \(q \Rightarrow \neg r\)  is not a tautology.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 17M.1.sl.TZ1.3a: Write down in words \(\neg q\).
• 17M.1.sl.TZ1.3b: Write down in symbolic form the compound statement: If I was paid then I completed the task.
• 17M.1.sl.TZ1.3c.i: Complete the following truth table.
• 17M.1.sl.TZ1.3c.ii: State whether the statements \(p \vee \neg q\) and \(q \Rightarrow p\) are logically equivalent....
• 17M.2.sl.TZ2.2a: Write down in symbolic form the compound proposition “If \(x\) is a factor of 60 then \(x\) is a...
• 17M.2.sl.TZ2.2b: Write down in words the compound proposition...
• 17M.2.sl.TZ2.2c: Copy the following truth table and complete the last three columns.
• 17M.2.sl.TZ2.2d: State why the compound proposition...
• 17M.2.sl.TZ2.2e: A row from the truth table from part (c) is given below. Write down one value of \(x\) that...
• 17N.1.sl.TZ0.4a: Write down in words \((q \vee \neg r) \Rightarrow p\).
• 17N.1.sl.TZ0.4b: Complete the truth table.
• 17N.1.sl.TZ0.4c: State whether the statement \(\neg p \Rightarrow \neg (q \vee \neg r)\) is the inverse, the...
• 18M.1.sl.TZ1.3a: Write down in words the compound proposition ¬\(p \Rightarrow q\).
• 18M.1.sl.TZ1.3b: Complete the truth table.
• 18M.1.sl.TZ1.3c: State whether the compound proposition (\(\neg p \Rightarrow q\)) ∨ (\(\neg p \wedge q\)) is a...
• 18M.1.sl.TZ2.2a: Write down, in words, \(\left( {q \wedge r} \right) \Rightarrow \neg p\).
• 18M.1.sl.TZ2.2b: Complete the following truth table.
• 18M.1.sl.TZ2.2c: State whether \(\left( {q \wedge r} \right) \Rightarrow \neg p\) is a tautology, contradiction or...

3.2

• 10M.1.sl.TZ1.3b: Decide whether the compound...
• 10M.1.sl.TZ2.2c: Consider the following propositions.      p: Feng finishes his homework      q: Feng goes to...
• 11N.1.sl.TZ0.3b.i: State whether the statement \((p \wedge q) \Rightarrow (\neg p \underline \vee q)\) is a logical...
• 10N.1.sl.TZ0.2b: Consider the propositions      p: Cristina understands logic      q: Cristina will do well on...
• 12N.1.sl.TZ0.9a: Write in words the compound statement \(\neg p \wedge q\) .
• 12N.1.sl.TZ0.9b: Write the following statement in symbolic form. “Either Carlos is playing the guitar or he is...
• 12N.1.sl.TZ0.9c: Write the converse of the following statement in symbolic form. “If Carlos is playing the guitar...
• 12M.1.sl.TZ1.6a: Write down, in words, the statement p \(\Rightarrow\) q.
• 12M.1.sl.TZ1.6b: Write down, in words, the inverse of the statement p \(\Rightarrow\) q.
• 12M.1.sl.TZ1.6c: State whether the inverse of the statement p \( \Rightarrow \) q is always true. Justify your...
• 12M.1.sl.TZ2.2b: Write the following compound proposition in symbolic form. “I cannot swim 50 metres and I take...
• 12M.1.sl.TZ2.2c: Write the following compound proposition in words. \(q \Rightarrow \neg q \)
• 09N.2.sl.TZ0.2B, a: Write the following compound statement in symbolic form. “It is snowing and the roads are not...
• 09N.2.sl.TZ0.2B, b: Write the following compound statement in words. \((\neg p \wedge q) \Rightarrow r\)
• 11M.1.sl.TZ1.4b: What Anna said was lost by the police, but in symbolic form it...
• 11M.1.sl.TZ1.4a: Write down Matthew’s statement in symbolic logic form.
• 09M.1.sl.TZ1.2a: Write in words the compound proposition \(p \Rightarrow q\) ;
• 09M.1.sl.TZ1.2b: Write in words the compound proposition \(\neg p \vee q\).
• 07N.1.sl.TZ0.7c: Complete the following truth table.
• 09M.2.sl.TZ2.4ii, a: Write in words \((q \wedge \neg r) \Rightarrow \neg p\).
• 09M.2.sl.TZ2.4ii, b, i: Consider the statement “If the number is a multiple of five, and is not even then it will not end...
• 11M.1.sl.TZ2.3a: Write, in words, the compound proposition\[\neg h \Rightarrow (p \vee a)\].
• 13M.1.sl.TZ1.3a: Write down the following compound propositions in symbolic form. (i) Yuiko is studying French...
• 13M.1.sl.TZ1.6b: Consider the propositions p and q: p: x is a number less than 10. q: x2 is a number greater...
• 13M.1.sl.TZ2.2a: Write the following compound proposition in symbolic form. If students do not stay up late then...
• 07M.1.sl.TZ0.4a: Explain the distinction between the compound propositions,...
• 07M.1.sl.TZ0.7b: Consider the propositions: p : x is a prime number less than 10. q : x is a positive integer...
• SPM.1.sl.TZ0.3a: Write the following argument in words\[\neg r \Rightarrow (q \vee p)\]
• SPM.1.sl.TZ0.10a: Express in words the statement, \(s \Rightarrow q\) .
• SPM.1.sl.TZ0.10b: Write down in words, the inverse of the statement, \(s \Rightarrow q\) .
• 07N.1.sl.TZ0.7a: Write the sentence above using logic symbols.
• 07N.1.sl.TZ0.7b: Write in words \(s \Rightarrow \neg d\) .
• 08N.1.sl.TZ0.4a: Complete the truth table below for the symbolic statement \(\neg (p \vee q)\) .
• 08N.1.sl.TZ0.4b: Write down in words the meaning of the symbolic statement \(\neg (p \vee q)\).
• 08N.1.sl.TZ0.4c: Write in symbolic form the compound statement: “no food and no drinks may be taken into the...
• 08M.1.sl.TZ1.6a: Write in words, \(p \underline { \vee } q\).
• 08M.1.sl.TZ1.6b: Write in words, the converse of \(p \Rightarrow \neg q\).
• 08M.1.sl.TZ1.6c: Complete the following truth table for \(p \Rightarrow \neg q\).
• 08M.1.sl.TZ2.1b: Consider the following propositions. \(p:{\text{ Amy eats sweets}}\) ...
• 09M.2.sl.TZ2.4ii, b, ii: Consider the statement “If the number is a multiple of five, and is not even then it will not end...
• 14M.1.sl.TZ2.2a: Write down the following statement in words. \[q \Rightarrow p\]
• 14M.1.sl.TZ2.2b: Write down, in words, the contrapositive statement of \(q \Rightarrow p\).
• 13N.1.sl.TZ0.3a: Write down, in words, the compound proposition \(\neg p \Rightarrow q\).
• 14M.1.sl.TZ1.3a: Write the following compound proposition in words. \[(p \wedge q) \Rightarrow \neg r\]
• 14M.1.sl.TZ1.14a: Express the following in symbolic form. “A rectangle always has two diagonals that are equal in...
• 14N.1.sl.TZ0.5a: Write down in words, the inverse of \(p \Rightarrow q\).
• 15M.1.sl.TZ2.5a: Complete the following truth table.
• 15M.1.sl.TZ2.11b: Write down in symbolic form the compound statement \(r:\) If \(x\) is a multiple of \(12\), then...
• 15M.1.sl.TZ2.11c: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 15M.1.sl.TZ2.11d: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 15M.1.sl.TZ2.11a: Write down in words \(\neg p\).
• 15M.2.sl.TZ1.2a: Write the following argument in symbolic form. “If the land has been purchased and the building...
• 15M.2.sl.TZ1.2d: Write down the inverse of the argument in part (a) (i)     in symbolic form; (ii)     in words.
• 16M.1.sl.TZ1.5a: Consider the following statements \(z\,:\,x\) is an integer\(q\,:\,x\) is a rational...
• 16M.1.sl.TZ1.5b: Write the following argument in symbolic form:“If \(x\) is a real number and \(x\) is not a...
• 16M.1.sl.TZ1.5c: Phoebe states that the argument in part (b) can be shown to be valid, without the need of a truth...
• 16N.1.sl.TZ0.5a: Write down in words the compound proposition
• 16N.1.sl.TZ0.5b: Complete the following truth table.
• 16N.1.sl.TZ0.5c: On a morning when Sandi does not get up before eight o’clock, use your truth table to determine...
• 16M.1.sl.TZ2.4a: Consider the following propositions: \(p:\) The lesson is cancelled \(q:\) The teacher is...
• 16M.1.sl.TZ2.4b: Complete the following truth table.
• 16M.1.sl.TZ2.4c: Hence, justify why \(q \Rightarrow \neg r\)  is not a tautology.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 17M.1.sl.TZ1.3a: Write down in words \(\neg q\).
• 17M.1.sl.TZ1.3b: Write down in symbolic form the compound statement: If I was paid then I completed the task.
• 17M.1.sl.TZ1.3c.i: Complete the following truth table.
• 17M.1.sl.TZ1.3c.ii: State whether the statements \(p \vee \neg q\) and \(q \Rightarrow p\) are logically equivalent....
• 17M.2.sl.TZ2.2a: Write down in symbolic form the compound proposition “If \(x\) is a factor of 60 then \(x\) is a...
• 17M.2.sl.TZ2.2b: Write down in words the compound proposition...
• 17M.2.sl.TZ2.2c: Copy the following truth table and complete the last three columns.
• 17M.2.sl.TZ2.2d: State why the compound proposition...
• 17M.2.sl.TZ2.2e: A row from the truth table from part (c) is given below. Write down one value of \(x\) that...
• 17N.1.sl.TZ0.4a: Write down in words \((q \vee \neg r) \Rightarrow p\).
• 17N.1.sl.TZ0.4b: Complete the truth table.
• 17N.1.sl.TZ0.4c: State whether the statement \(\neg p \Rightarrow \neg (q \vee \neg r)\) is the inverse, the...
• 18M.1.sl.TZ1.3a: Write down in words the compound proposition ¬\(p \Rightarrow q\).
• 18M.1.sl.TZ1.3b: Complete the truth table.
• 18M.1.sl.TZ1.3c: State whether the compound proposition (\(\neg p \Rightarrow q\)) ∨ (\(\neg p \wedge q\)) is a...
• 18M.1.sl.TZ2.2a: Write down, in words, \(\left( {q \wedge r} \right) \Rightarrow \neg p\).
• 18M.1.sl.TZ2.2b: Complete the following truth table.
• 18M.1.sl.TZ2.2c: State whether \(\left( {q \wedge r} \right) \Rightarrow \neg p\) is a tautology, contradiction or...

3.3

• 10M.1.sl.TZ1.3a: Complete the truth table below.
• 10M.1.sl.TZ1.3b: Decide whether the compound...
• 10M.1.sl.TZ2.2a: Complete the truth table shown below.
• 10M.1.sl.TZ2.2b: State whether the compound proposition \((p \vee (p \wedge q)) \Rightarrow p\) is a...
• 11N.1.sl.TZ0.3a: Complete the truth table below.
• 11N.1.sl.TZ0.3b.i: State whether the statement \((p \wedge q) \Rightarrow (\neg p \underline \vee q)\) is a logical...
• 11N.1.sl.TZ0.3b.ii: Give a reason for your answer to part (b)(i).
• 10N.1.sl.TZ0.2a: Complete the following truth table.
• 12M.1.sl.TZ2.2a: Complete the truth table below.
• 09N.2.sl.TZ0.2B, c: An incomplete truth table for the compound proposition \((\neg p \wedge q) \Rightarrow r\) is...
• 09M.1.sl.TZ1.2c: The truth table for these compound propositions is given below. Complete the column for...
• 13M.1.sl.TZ1.6a: Complete the truth table.
• 13M.1.sl.TZ2.2b: Complete the following truth table.
• 07N.1.sl.TZ0.7c: Complete the following truth table.
• 11M.1.sl.TZ2.3b: Complete the truth table for \(\neg a \Rightarrow p\) .
• 11M.1.sl.TZ2.3c: State whether \(\neg a \Rightarrow p\) is a tautology, a contradiction or neither. Justify your...
• 13M.1.sl.TZ2.2c: Write down a reason why the statement \(\neg ( p \vee \neg q)\) is not a contradiction.
• 07M.1.sl.TZ0.4b: Fill in the four missing truth-values on the table.
• 07M.1.sl.TZ0.4c: State whether the proposition...
• SPM.1.sl.TZ0.3b: Complete the truth table for the argument in part (a) using the values below for \(p\) , \(q\) ,...
• 08N.1.sl.TZ0.4a: Complete the truth table below for the symbolic statement \(\neg (p \vee q)\) .
• 08M.1.sl.TZ1.6c: Complete the following truth table for \(p \Rightarrow \neg q\).
• 08M.1.sl.TZ2.1a: (i)     Complete the truth table below. (ii)    State whether the compound propositions...
• 13N.1.sl.TZ0.3b: Complete the truth table.
• 14M.1.sl.TZ1.3b: Complete the following truth table.
• 14N.1.sl.TZ0.5b: Complete the following truth table.
• 14N.1.sl.TZ0.5c: State whether the converse and the inverse of an implication are logically equivalent. Justify...
• 15M.1.sl.TZ2.5a: Complete the following truth table.
• 15M.1.sl.TZ2.5b: Determine whether the compound proposition...
• 15M.2.sl.TZ1.2b: In your answer booklet, copy and complete a truth table for the argument in part (a). Begin your...
• 16N.1.sl.TZ0.5a: Write down in words the compound proposition
• 16N.1.sl.TZ0.5b: Complete the following truth table.
• 16N.1.sl.TZ0.5c: On a morning when Sandi does not get up before eight o’clock, use your truth table to determine...
• 16M.1.sl.TZ2.4a: Consider the following propositions: \(p:\) The lesson is cancelled \(q:\) The teacher is...
• 16M.1.sl.TZ2.4b: Complete the following truth table.
• 16M.1.sl.TZ2.4c: Hence, justify why \(q \Rightarrow \neg r\)  is not a tautology.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 17M.1.sl.TZ1.3a: Write down in words \(\neg q\).
• 17M.1.sl.TZ1.3b: Write down in symbolic form the compound statement: If I was paid then I completed the task.
• 17M.1.sl.TZ1.3c.i: Complete the following truth table.
• 17M.1.sl.TZ1.3c.ii: State whether the statements \(p \vee \neg q\) and \(q \Rightarrow p\) are logically equivalent....
• 17M.2.sl.TZ2.2a: Write down in symbolic form the compound proposition “If \(x\) is a factor of 60 then \(x\) is a...
• 17M.2.sl.TZ2.2b: Write down in words the compound proposition...
• 17M.2.sl.TZ2.2c: Copy the following truth table and complete the last three columns.
• 17M.2.sl.TZ2.2d: State why the compound proposition...
• 17M.2.sl.TZ2.2e: A row from the truth table from part (c) is given below. Write down one value of \(x\) that...
• 17N.1.sl.TZ0.4a: Write down in words \((q \vee \neg r) \Rightarrow p\).
• 17N.1.sl.TZ0.4b: Complete the truth table.
• 17N.1.sl.TZ0.4c: State whether the statement \(\neg p \Rightarrow \neg (q \vee \neg r)\) is the inverse, the...
• 18M.1.sl.TZ1.3a: Write down in words the compound proposition ¬\(p \Rightarrow q\).
• 18M.1.sl.TZ1.3b: Complete the truth table.
• 18M.1.sl.TZ1.3c: State whether the compound proposition (\(\neg p \Rightarrow q\)) ∨ (\(\neg p \wedge q\)) is a...
• 18M.1.sl.TZ2.2a: Write down, in words, \(\left( {q \wedge r} \right) \Rightarrow \neg p\).
• 18M.1.sl.TZ2.2b: Complete the following truth table.
• 18M.1.sl.TZ2.2c: State whether \(\left( {q \wedge r} \right) \Rightarrow \neg p\) is a tautology, contradiction or...

3.4

• 10N.1.sl.TZ0.2c: Write down in words the contrapositive of the proposition given in part (b).
• 12N.1.sl.TZ0.9c: Write the converse of the following statement in symbolic form. “If Carlos is playing the guitar...
• 12M.1.sl.TZ1.6b: Write down, in words, the inverse of the statement p \(\Rightarrow\) q.
• 12M.1.sl.TZ1.6c: State whether the inverse of the statement p \( \Rightarrow \) q is always true. Justify your...
• 09N.1.sl.TZ0.7a: Write down the inverse of statement p in words.
• 09N.1.sl.TZ0.7b: Write down the converse of statement p in words.
• 09N.1.sl.TZ0.7c: Determine whether the converse of statement p is always true. Give an example to justify your...
• 09M.1.sl.TZ1.2d: The truth table for these compound propositions is given below. State the relationship between...
• 13M.1.sl.TZ1.3b: Write down in words the inverse of the following compound proposition. If Yuiko is studying...
• 13M.1.sl.TZ1.6c: Using part (a), determine whether \(\neg p \vee q\) is true or false, for the case where \(x\) is...
• 13M.1.sl.TZ1.6d: Write down a value of \(x\) for which \(\neg p \vee q\) is false.
• SPM.1.sl.TZ0.3c: The argument \(\neg r \Rightarrow (q \vee p)\) is invalid. State the reason for this.
• SPM.1.sl.TZ0.10b: Write down in words, the inverse of the statement, \(s \Rightarrow q\) .
• SPM.1.sl.TZ0.10c: Determine the validity of the argument in (b). Give a reason for your decision.
• 08M.1.sl.TZ2.1a: (i)     Complete the truth table below. (ii)    State whether the compound propositions...
• 14M.1.sl.TZ2.2b: Write down, in words, the contrapositive statement of \(q \Rightarrow p\).
• 14M.1.sl.TZ2.2c: Determine whether your statement in part (a) is logically equivalent to your statement in part...
• 13N.1.sl.TZ0.3c: Write down, in symbolic form, the converse of \(\neg p \Rightarrow q\).
• 14M.1.sl.TZ1.14b: Write down in symbolic form the converse of the statement in (a).
• 14M.1.sl.TZ1.14c: Determine, without using a truth table, whether the statements in (a) and (b) are logically...
• 14M.1.sl.TZ1.14d: Write down the name of the statement that is logically equivalent to the converse.
• 14N.1.sl.TZ0.5a: Write down in words, the inverse of \(p \Rightarrow q\).
• 14N.1.sl.TZ0.5b: Complete the following truth table.
• 14N.1.sl.TZ0.5c: State whether the converse and the inverse of an implication are logically equivalent. Justify...
• 15M.1.sl.TZ2.11c: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 15M.1.sl.TZ2.11d: Consider the compound statement \(s:\) If \(x\) is a multiple of \(6\), then \(x\) is a multiple...
• 15M.2.sl.TZ1.2c: Use your truth table to determine whether the argument in part (a) is valid. Give a reason for...
• 15M.2.sl.TZ1.2d: Write down the inverse of the argument in part (a) (i)     in symbolic form; (ii)     in words.
• 16N.1.sl.TZ0.5a: Write down in words the compound proposition
• 16N.1.sl.TZ0.5b: Complete the following truth table.
• 16N.1.sl.TZ0.5c: On a morning when Sandi does not get up before eight o’clock, use your truth table to determine...
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 17M.1.sl.TZ1.3a: Write down in words \(\neg q\).
• 17M.1.sl.TZ1.3b: Write down in symbolic form the compound statement: If I was paid then I completed the task.
• 17M.1.sl.TZ1.3c.i: Complete the following truth table.
• 17M.1.sl.TZ1.3c.ii: State whether the statements \(p \vee \neg q\) and \(q \Rightarrow p\) are logically equivalent....
• 17N.1.sl.TZ0.4a: Write down in words \((q \vee \neg r) \Rightarrow p\).
• 17N.1.sl.TZ0.4b: Complete the truth table.
• 17N.1.sl.TZ0.4c: State whether the statement \(\neg p \Rightarrow \neg (q \vee \neg r)\) is the inverse, the...

3.5

• 10M.1.sl.TZ1.2: The sets \(P\), \(Q\) and \(U\) are defined as U = {Real Numbers} ,  P = {Positive Numbers} and...
• 10M.1.sl.TZ1.6a: Write down the value of q.
• 10M.1.sl.TZ1.6b: Find the value of p.
• 10M.1.sl.TZ1.6c: Calculate the number of members of the fitness club who attend neither the aerobics course (A)...
• 10M.1.sl.TZ1.6d: Shade, on your Venn diagram, \(A' \cap Y\) .
• 10M.1.sl.TZ2.6a: Show this information on the Venn diagram below.
• 10M.1.sl.TZ2.6b: Find the number of students who like both peanut butter and jam.
• 10M.1.sl.TZ2.8a: Find \({\text{P}}(A \cap B)\).
• 10M.1.sl.TZ2.8b: Find \({\text{P}}(A|B)\).
• 11N.1.sl.TZ0.5a: Find the number that have both Australian and British passports.
• 11N.1.sl.TZ0.5b: In the Venn diagram below, set A represents the people in the group with Australian passports and...
• 11N.1.sl.TZ0.5c: In the Venn diagram below, set A represents the people in the group with Australian passports and...
• 10N.1.sl.TZ0.9a.i: List the elements of the following set. A
• 10N.1.sl.TZ0.9b: Write down one element of \((A \cup B)'\).
• 10N.1.sl.TZ0.9c: One of the statements in the table below is false. Indicate with an X which statement is false....
• 10N.2.sl.TZ0.1A.a: Represent this information on a Venn diagram.
• 10N.2.sl.TZ0.1A.b: Find the number of students who had none of the three choices for breakfast.
• 10N.2.sl.TZ0.1A.c: Write down the percentage of students who had fruit for breakfast.
• 10N.2.sl.TZ0.1A.d: Describe in words what the students in the set \(X \cap Y'\) had for breakfast.
• 10N.2.sl.TZ0.1A.e: Find the probability that a student had at least two of the three choices for breakfast.
• 10N.2.sl.TZ0.1A.f: Two students are chosen at random. Find the probability that both students had all three choices...
• 12N.2.sl.TZ0.2a: Draw a Venn diagram to show this information. Use T to represent the set of students who have a...
• 12N.2.sl.TZ0.2b: Write down the number of students that (i) have a computer only; (ii) have an iPhone and a...
• 12N.2.sl.TZ0.2c: Write down \(n[T \cap (C \cup I)']\).
• 12N.2.sl.TZ0.2d: Calculate the number of students who have none of the three.
• 12M.2.sl.TZ1.1a: Draw a Venn diagram to represent this information. Label A the set that represents The Art...
• 12M.2.sl.TZ1.1b: Find the percentage of the population that does not read any of the three newspapers.
• 12M.2.sl.TZ1.1c: Find the percentage of the population that reads exactly one newspaper.
• 12M.2.sl.TZ1.1d: Find the percentage of the population that reads The Art Journal or The Beartown News but not The...
• 12M.2.sl.TZ1.1e: A local radio station states that 83 % of the population reads either The Beartown News or The...
• 12M.1.sl.TZ2.4a: Write down the total number of students in the school.
• 12M.1.sl.TZ2.4b: Write down the number of students who (i) learn violin only; (ii) learn piano or flute or...
• 12M.1.sl.TZ2.4c: Explain, in words, the meaning of the part of the diagram that represents the set \(P \cap F'\).
• 09N.1.sl.TZ0.2: The Venn diagram shows the number sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and...
• 09N.1.sl.TZ0.14a: Draw a Venn diagram in the space below to illustrate this information.
• 09N.1.sl.TZ0.14b: Find the probability that a student studies Spanish given that she studies one language only.
• 09N.2.sl.TZ0.2A, a: Copy and complete the Venn diagram on your answer paper.
• 09N.2.sl.TZ0.2A, b: Write down the number of students who study Mathematics but not Further Mathematics.
• 09N.2.sl.TZ0.2A, c: Write down the total number of students in the school.
• 09N.2.sl.TZ0.2A, d: Write down \(n({\text{B}} \cup {\text{C}})\).
• 09M.2.sl.TZ1.2ii, a: Write down \(n(R \cap S \cap B)\).
• 09M.2.sl.TZ1.2ii, b: Find \(n(R')\).
• 09M.2.sl.TZ1.2ii, c: Describe which groups the pupils in the set \(S \cap B\) like.
• 09M.2.sl.TZ1.2ii, d: Use set notation to describe the group of pupils who like the Rockers and the Bluers but do not...
• 09M.2.sl.TZ1.2ii, e, i: There are 33 pupils in the class. Find x.
• 09M.2.sl.TZ2.1a: Draw a Venn diagram to represent this information.
• 13M.1.sl.TZ1.2b: Write down the elements of U on the Venn diagram.
• 11M.2.sl.TZ1.2A.a: Draw a Venn Diagram, using sets labelled \(A\) , \(S\) and \(P\) , that shows this information.
• 13M.2.sl.TZ1.2a: Draw a Venn diagram to represent the information above.
• 13M.2.sl.TZ2.1a: Draw a Venn diagram to represent the given information using sets labelled C, M and P. Complete...
• 11M.2.sl.TZ1.2A.b: There were 48 customers of Pete’s Eats that day. Calculate the number of people who were...
• 11M.2.sl.TZ1.2A.c: There were 50 customers of Sarah’s Snackbar that day. Calculate the total number of people who...
• 11M.2.sl.TZ1.2A.d: Write down the number of customers of Alan’s Diner that were also customers of Pete’s Eats.
• 11M.2.sl.TZ1.2A.e: Find \(n[(S \cup P) \cap A']\).
• 07N.1.sl.TZ0.8a: Enter the above information on the Venn diagram below.
• 09M.2.sl.TZ2.1b: Find the number of families who own no pets.
• 11M.1.sl.TZ2.1a: Write down the number of elements in \(A \cap C\) .
• 11M.1.sl.TZ2.1c: Complete the following Venn diagram with all the elements of \(U\) .
• 13M.1.sl.TZ1.2a: List the elements of (i) U ; (ii) B .
• 13M.1.sl.TZ1.2c: Write down \(n (A \cap B)\).
• 13M.2.sl.TZ1.2b: Write down the number of students who study Music but not Economics.
• 13M.2.sl.TZ1.2c: There are 22 Economics students in total. (i) Calculate the number of students who study...
• 13M.2.sl.TZ2.1b: Find the number of families who (i) went to the circus only; (ii) went to the museum and the...
• 07M.1.sl.TZ0.7a: List the members of sets (i) \(B\) (ii) \(C \cap B\) (iii) \(B \cup C′\)
• SPM.2.sl.TZ0.5a: Represent this information on a Venn Diagram.
• SPM.2.sl.TZ0.5b: There were \(28\) students who used a bus to travel to school. Calculate the number of...
• SPM.2.sl.TZ0.5c: Tomoko used a bus to travel to school yesterday. Find the probability that she also walked.
• SPM.2.sl.TZ0.5d: Two students are chosen at random from all \(50\) students. Find the probability that(i)    ...
• 07M.2.sl.TZ0.5ii.a: Complete the diagram, using the information given in the question.
• 07M.2.sl.TZ0.5ii.b: Find (i) \(n(M \cap W)\) (ii) \(n(M′ \cup S)\)
• 07N.1.sl.TZ0.2a: List the elements of the following sets: A,
• 07N.1.sl.TZ0.2b: List the elements of the following sets: B,
• 07N.1.sl.TZ0.2c: List the elements of the following sets: \(A \cup B\) ,
• 07N.1.sl.TZ0.2d: List the elements of the following sets: \(A \cap B'\) .
• 07N.1.sl.TZ0.8b: 99 of the students play basketball, 88 sing in the choir and 110 do drama. Calculate the number...
• 07N.1.sl.TZ0.8c: 99 of the students play basketball, 88 sing in the choir and 110 do drama. Calculate the total...
• 08N.1.sl.TZ0.9a: Write down the number of pupils that study Chemistry only.
• 08N.1.sl.TZ0.9b: Write down the number of pupils that study exactly two sciences.
• 08N.1.sl.TZ0.9c: Write down the number of pupils that do not study Physics.
• 08N.1.sl.TZ0.9d: Find \(n[(P \cup B) \cap C]\) .
• 08M.2.sl.TZ1.2i.a: Represent this information on a Venn diagram.
• 08M.2.sl.TZ1.2i.b: Calculate the number of students who own none of the items mentioned above.
• 08M.1.sl.TZ2.9a: Shade \((A \cup B) \cap C'\) on the diagram below.
• 08M.1.sl.TZ2.9b: In the Venn diagram below, the number of elements in each region is given. Find...
• 08M.1.sl.TZ2.9c: \(U\) is the set of positive integers, \({\mathbb{Z}^ + }\). \(E\) is the set of even...
• 09M.2.sl.TZ1.2ii, e, ii: There are 33 pupils in the class. Find the number of pupils who like the Rockers.
• 10N.1.sl.TZ0.9a.ii: List the elements of the following set. \(A \cap B'\)
• 14M.1.sl.TZ2.3a: 4
• 14M.1.sl.TZ2.3b: \(\frac{1}{3}\)
• 14M.1.sl.TZ2.3c: \(\pi \)
• 14M.1.sl.TZ2.3d: \(0.38\)
• 14M.1.sl.TZ2.3e: \(\sqrt 5 \)
• 14M.1.sl.TZ2.3f: \(-0.25\)
• 13N.1.sl.TZ0.2a: List the elements of \(A\).
• 13N.1.sl.TZ0.2b: List the elements of \(B\).
• 13N.1.sl.TZ0.2c: Complete the Venn diagram with all the elements of \(U\).
• 13N.2.sl.TZ0.3a: Draw a Venn diagram, using sets labelled \(E\), \(S\) and \(A\), to show this information.
• 13N.2.sl.TZ0.3b: Calculate the value of \(x\).
• 13N.2.sl.TZ0.3c: Explain, in words, the meaning of \((E \cup S) \cap A'\).
• 13N.2.sl.TZ0.3d: Write down \(n\left( {(E \cup S \cup A)'} \right)\).
• 14M.2.sl.TZ1.2a: Draw a Venn diagram to show this information.
• 14M.2.sl.TZ1.2b: There were 25 tourists in the group and every tourist saw at least one of the three types of...
• 14N.1.sl.TZ0.8a: Complete the Venn diagram by placing the letter corresponding to each polygon in the appropriate...
• 14N.1.sl.TZ0.8b: State which polygons from Tuti’s list are elements of (i)     \(A \cap B\); (ii)    ...
• 15M.1.sl.TZ1.8a: Complete the Venn diagram with the numbers written on Aleph’s die (\(A\)) and Beth’s die (\(B\)).
• 15M.1.sl.TZ1.8b: Find \(n(B \cap A')\).
• 15M.1.sl.TZ2.6: Consider the following Venn diagrams. Each diagram is shaded differently. In the following...
• 15M.2.sl.TZ2.1a: Copy the following Venn diagram and correctly insert all values from the above information.
• 15M.2.sl.TZ2.1b: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1c: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1d: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1e: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1f: The number of customers that like only mangoes is equal to the number of customers that like only...
• 16M.2.sl.TZ1.2a: A group of students at Dune Canyon High School were surveyed. They were asked which of the...
• 16M.2.sl.TZ1.2b: Calculate the number of students who were surveyed.
• 16M.2.sl.TZ1.2c: i)     On your Venn diagram, shade the set \({\left( {F \cup M} \right) \cap B'}\) . Do not shade...
• 16M.2.sl.TZ1.2d: A student who was surveyed is chosen at random. Find the probability that (i)     the student...
• 16M.2.sl.TZ1.2e: Dune Canyon High School has 850 students. Find the expected number of students at Dune Canyon...
• 16N.1.sl.TZ0.3a: In the table indicate whether the given statements are True or False.
• 16N.1.sl.TZ0.3b: On the Venn diagram, shade the region \(A \cap (B \cup C)'\).
• 16N.2.sl.TZ0.2a: Draw a Venn diagram to represent the given information, using sets labelled \(B\), \(C\) and \(H\).
• 16N.2.sl.TZ0.2b: Show that \(x = 3\).
• 16N.2.sl.TZ0.2c: Write down the value of \(n(B \cap C)\).
• 16N.2.sl.TZ0.2d: Find the probability that this person (i)     went on at most one trip; (ii)     went on the...
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 16M.2.sl.TZ2.1a: \(180\) people were interviewed and asked what types of transport they had used in the last year...
• 16M.2.sl.TZ2.1b: Find the number of people who, in the last year, had travelled by (i)      bus only; (ii)  ...
• 16M.2.sl.TZ2.1c: A person is selected at random from those who were interviewed. Find the probability that the...
• 16M.2.sl.TZ2.1d: Given that the person had used only one type of transport in the last year, find the probability...
• 17M.1.sl.TZ1.4a: Write down the number of sporting activities offered by the school during its school year.
• 17M.1.sl.TZ1.4b: Determine whether rock-climbing is offered by the school in the fall/autumn trimester.
• 17M.1.sl.TZ1.4c.i: Write down the elements of the set \(F \cap W’\);
• 17M.1.sl.TZ1.4c.ii: Write down \(n(W \cap S)\).
• 17M.1.sl.TZ1.4d: Write down, in terms of \(F\), \(W\) and \(S\), an expression for the set which contains only...
• 17M.1.sl.TZ2.2a: Write down an expression, in terms of \(x\), for the number of children who play only basketball.
• 17M.1.sl.TZ2.2b: Complete the Venn diagram using the above information.
• 17M.1.sl.TZ2.2c: Find the number of children who play only football.
• 17M.1.sl.TZ2.2d: Write down the value of \(n(F)\).
• 17N.1.sl.TZ0.7a: Complete the Venn diagram for these students.
• 17N.1.sl.TZ0.7b: One of the students who joined the sports club is chosen at random. Find the probability that...
• 17N.1.sl.TZ0.7c: Determine whether the events \(S\) and \(M\) are independent.
• 18M.1.sl.TZ1.10a: Complete the Venn diagram using the given information.
• 18M.1.sl.TZ1.10b: Find the value of x.
• 18M.1.sl.TZ1.10c: Write down the value of \(n\left( {\left( {F \cup H} \right) \cap S'} \right)\).
• 18M.1.sl.TZ2.9a.i: Write down an expression, in set notation, for the shaded region represented by Diagram 1.
• 18M.1.sl.TZ2.9a.ii: Write down an expression, in set notation, for the shaded region represented by Diagram 2.
• 18M.1.sl.TZ2.9a.iii: Write down an expression, in set notation, for the shaded region represented by Diagram 3.
• 18M.1.sl.TZ2.9b.i: Shade, on the Venn diagram, the region represented by the set \(\left( {H \cup I} \right)'\).  
• 18M.1.sl.TZ2.9b.ii: Shade, on the Venn diagram, the region represented by the set \(J \cap K\).
• 18M.2.sl.TZ2.1a.i: Write down the value of a.
• 18M.2.sl.TZ2.1a.ii: Write down the value of b.
• 18M.2.sl.TZ2.1b.i: Use the tree diagram to find the probability that an employee encountered traffic and was late...
• 18M.2.sl.TZ2.1b.ii: Use the tree diagram to find the probability that an employee was late for work.
• 18M.2.sl.TZ2.1b.iii: Use the tree diagram to find the probability that an employee encountered traffic given that they...
• 18M.2.sl.TZ2.1c.i: Find the value of x.
• 18M.2.sl.TZ2.1c.ii: Find the value of y.
• 18M.2.sl.TZ2.1d: Find the number of employees who, in the last year, did not travel to work by car, bicycle or...
• 18M.2.sl.TZ2.1e: Find \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).

3.6

• 11N.1.sl.TZ0.10a: Write down the probability that (i) Ju Shen chooses a red disc from the bag; (ii) Ramón chooses...
• 12N.2.sl.TZ0.4a: Use the table to find the probability that (i) a television will be bought by a female; (ii) a...
• 12M.2.sl.TZ2.1b: Leanne catches a fish. Find the probability that she (i) catches an undersized bream; (ii)...
• 12M.2.sl.TZ2.1c: Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy...
• 11N.2.sl.TZ0.2a: A student is chosen at random from the group. Find the probability that the student (i)    ...
• 09M.1.sl.TZ1.11a: Find the probability that the two dice show the same number.
• 09M.2.sl.TZ1.2i, c: Find the probability that they do not have pasta.
• 09M.2.sl.TZ1.2ii, b: Find \(n(R')\).
• 07N.2.sl.TZ0.1i.a: Copy the tree diagram below and fill in all the probabilities, where NL represents not late, to...
• 11M.2.sl.TZ1.2B.a: One of the survey forms was chosen at random, find the probability that the form showed...
• 09M.2.sl.TZ2.1c: Find the percentage of families that own exactly one pet.
• 09M.1.sl.TZ2.13a: Find the value of (i)     m; (ii)     n.
• 13M.2.sl.TZ1.2d: A student is chosen at random from the 100 that were asked above. Find the probability that this...
• 13M.1.sl.TZ2.10a: Write down the probability that the sock is red.
• 13M.2.sl.TZ2.1c: A family is chosen at random from the group of 40 families. Find the probability that the family...
• 07M.2.sl.TZ0.1d: The fishing company must pay a fine if more than 10% of the catch have lengths less than...
• 07M.2.sl.TZ0.5i.a: One of the dogs is chosen at random. (i) Find P (the dog is grey and has the yellow bowl). (ii)...
• 07N.2.sl.TZ0.1i.b: Find the probability that Geraldine travels by bus and is late.
• 08N.2.sl.TZ0.3b: Consider the \(200\) drivers surveyed. One driver is chosen at random. Calculate the probability...
• 08M.1.sl.TZ1.9c: The maximum word count is \(4000\) words. Write down the probability that a student chosen at...
• 08M.2.sl.TZ1.2i.c: If a student is chosen at random, write down the probability that the student owns a digital...
• 08M.2.sl.TZ1.2ii.b: Calculate the probability that (i)     Kate goes to the cinema and is not late; (ii)    the...
• 08M.1.sl.TZ2.2d: Gabriel chooses a chicken at random. Find the probability that this chicken weighs less than...
• 08M.2.sl.TZ2.2i.a: One person is chosen at random from those surveyed. Find the probability that this person (i)...
• 14M.2.sl.TZ2.1a: Find the value of (i)     \({\text{A}}\); (ii)     \({\text{B}}\); (iii)     \({\text{C}}\).
• 14M.2.sl.TZ1.2c: There were 25 tourists in the group and every tourist saw at least one of the three types of...
• 14N.2.sl.TZ0.2a: Write down the value of (i)     \(p\) ; (ii)     \(q\) ; (iii)     \(r\).
• 14N.2.sl.TZ0.2b: (i)     Find the probability that Mike reaches Trap B. (ii)     Find the probability that Mike...
• 15M.1.sl.TZ1.2c: Find the probability that a student chosen at random from the group scored at least a grade \(4\).
• 15M.1.sl.TZ1.11a: On a day chosen at random, Peter walked to work. Write down the probability that he was on time.
• 16M.1.sl.TZ1.1a: The probability that Nikita wins a tennis match depends on the surface of the tennis court on...
• 16M.1.sl.TZ1.1b: Find the probability that Nikita wins a match.
• 16M.2.sl.TZ1.2a: A group of students at Dune Canyon High School were surveyed. They were asked which of the...
• 16M.2.sl.TZ1.2b: Calculate the number of students who were surveyed.
• 16M.2.sl.TZ1.2c: i)     On your Venn diagram, shade the set \({\left( {F \cup M} \right) \cap B'}\) . Do not shade...
• 16M.2.sl.TZ1.2d: A student who was surveyed is chosen at random. Find the probability that (i)     the student...
• 16M.2.sl.TZ1.2e: Dune Canyon High School has 850 students. Find the expected number of students at Dune Canyon...
• 16M.1.sl.TZ2.5a: Two friends, Sensen and Cruz, are conducting an investigation on probability. Sensen has a fair...
• 16M.1.sl.TZ2.5b: Find the probability that the number shown on the die is \(1\) or the colour shown on the disc is...
• 16M.1.sl.TZ2.5c: Find the probability that the number shown on the die is even given that the colour shown on the...
• 16N.2.sl.TZ0.2a: Draw a Venn diagram to represent the given information, using sets labelled \(B\), \(C\) and \(H\).
• 16N.2.sl.TZ0.2b: Show that \(x = 3\).
• 16N.2.sl.TZ0.2c: Write down the value of \(n(B \cap C)\).
• 16N.2.sl.TZ0.2d: Find the probability that this person (i)     went on at most one trip; (ii)     went on the...
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 16M.2.sl.TZ2.1a: \(180\) people were interviewed and asked what types of transport they had used in the last year...
• 16M.2.sl.TZ2.1b: Find the number of people who, in the last year, had travelled by (i)      bus only; (ii)  ...
• 16M.2.sl.TZ2.1c: A person is selected at random from those who were interviewed. Find the probability that the...
• 16M.2.sl.TZ2.1d: Given that the person had used only one type of transport in the last year, find the probability...
• 17N.1.sl.TZ0.7a: Complete the Venn diagram for these students.
• 17N.1.sl.TZ0.7b: One of the students who joined the sports club is chosen at random. Find the probability that...
• 17N.1.sl.TZ0.7c: Determine whether the events \(S\) and \(M\) are independent.
• 17N.2.sl.TZ0.4a: Find the probability that this person is not allergic to nuts.
• 17N.2.sl.TZ0.4b: Find the probability that both people chosen are not allergic to nuts.
• 17N.2.sl.TZ0.4c: Copy and complete the tree diagram.
• 17N.2.sl.TZ0.4d: Find the probability that this adult is allergic to nuts and the liquid turns blue.
• 17N.2.sl.TZ0.4e: Find the probability that the liquid turns blue.
• 17N.2.sl.TZ0.4f: Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.
• 17N.2.sl.TZ0.4g: Estimate the number of employees, from this 38, who are allergic to nuts.
• 18M.2.sl.TZ1.2a: State the alternative hypothesis.
• 18M.2.sl.TZ1.2b: Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.
• 18M.2.sl.TZ1.2c: Write down the number of degrees of freedom.
• 18M.2.sl.TZ1.2d.i: Write down the χ2 statistic.
• 18M.2.sl.TZ1.2d.ii: Write down the associated p-value.
• 18M.2.sl.TZ1.2e: State, with a reason, whether you would reject the null hypothesis.
• 18M.2.sl.TZ1.2f: Write down the probability that this flight arrived on time.
• 18M.2.sl.TZ1.2h: Two flights are chosen at random from those which were slightly delayed. Find the probability...
• 18M.2.sl.TZ1.5a: Write down the probability that Ayako avoids the trap in this wall.
• 18M.2.sl.TZ1.5b: Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to...
• 18M.2.sl.TZ1.5c: Copy the probability tree diagram and write down the relevant probabilities along the branches.
• 18M.2.sl.TZ1.5d.i: A contestant is chosen at random. Find the probability that this contestant fell into a trap...
• 18M.2.sl.TZ1.5d.ii: A contestant is chosen at random. Find the probability that this contestant fell into a trap.
• 18M.2.sl.TZ1.5e: 120 contestants attempted this game. Find the expected number of contestants who fell into a...
• 18M.1.sl.TZ2.7a: State the number of boys who answered questions in Portuguese.
• 18M.1.sl.TZ2.7b: Find the probability that the boy answered questions in Hindi.
• 18M.1.sl.TZ2.7c: Two girls are selected at random. Calculate the probability that one girl answered questions in...
• 18M.2.sl.TZ2.1a.i: Write down the value of a.
• 18M.2.sl.TZ2.1a.ii: Write down the value of b.
• 18M.2.sl.TZ2.1b.i: Use the tree diagram to find the probability that an employee encountered traffic and was late...
• 18M.2.sl.TZ2.1b.ii: Use the tree diagram to find the probability that an employee was late for work.
• 18M.2.sl.TZ2.1b.iii: Use the tree diagram to find the probability that an employee encountered traffic given that they...
• 18M.2.sl.TZ2.1c.i: Find the value of x.
• 18M.2.sl.TZ2.1c.ii: Find the value of y.
• 18M.2.sl.TZ2.1d: Find the number of employees who, in the last year, did not travel to work by car, bicycle or...
• 18M.2.sl.TZ2.1e: Find \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).

3.7

• 10M.1.sl.TZ1.8a: Complete the tree diagram below, showing the appropriate probabilities.
• 10M.1.sl.TZ1.8b: Find the probability that Maria is late for school.
• 10M.1.sl.TZ1.13a: Find the probability that a student chosen at random is male.
• 10M.1.sl.TZ1.13b: Find the probability that a student chosen at random is either male or studies Chemistry.
• 10M.1.sl.TZ1.13c: Find the probability that a student chosen at random studies Physics, given that the student is...
• 10M.1.sl.TZ2.6c: Find the probability that a randomly chosen student from the group likes peanut butter, given...
• 10M.1.sl.TZ2.8a: Find \({\text{P}}(A \cap B)\).
• 10M.1.sl.TZ2.8b: Find \({\text{P}}(A|B)\).
• 10M.1.sl.TZ2.8c: Decide whether A and B are independent events. Give a reason for your answer.
• 11N.1.sl.TZ0.10a: Write down the probability that (i) Ju Shen chooses a red disc from the bag; (ii) Ramón chooses...
• 11N.1.sl.TZ0.10b: Find the probability that Ju Shen and Ramón choose different coloured discs from the bag.
• 10N.1.sl.TZ0.6a: Write down the probability that this person is a smoker.
• 10N.1.sl.TZ0.6b: Write down the probability that this person is male given that they are a smoker.
• 10N.1.sl.TZ0.6c: Find the probability that this person is a smoker or is male.
• 10N.2.sl.TZ0.1A.e: Find the probability that a student had at least two of the three choices for breakfast.
• 10N.2.sl.TZ0.1A.f: Two students are chosen at random. Find the probability that both students had all three choices...
• 12N.2.sl.TZ0.2e: Two students are chosen at random from the 450 students. Calculate the probability that (i)...
• 12N.2.sl.TZ0.4a: Use the table to find the probability that (i) a television will be bought by a female; (ii) a...
• 12M.1.sl.TZ1.12a: Complete the tree diagram below.
• 12M.1.sl.TZ1.12b: Find the probability that Merryn will not be late for the concert.
• 12M.1.sl.TZ1.12c: Merryn was not late for the concert the next day. Given that, find the probability that she...
• 10M.2.sl.TZ2.1a.i: Write down the value of a.
• 10M.2.sl.TZ2.1b: Copy and complete the tree diagram below.
• 10M.2.sl.TZ2.1c.i: Find the probability that he chooses a chocolate biscuit.
• 12M.2.sl.TZ1.2g: One student is chosen at random from the 120 students. Find the probability that this...
• 12M.2.sl.TZ1.2h: Two students are chosen at random from the 120 students. Find the probability that (i) both...
• 12M.2.sl.TZ2.1b: Leanne catches a fish. Find the probability that she (i) catches an undersized bream; (ii)...
• 12M.2.sl.TZ2.1c: Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy...
• 12M.2.sl.TZ2.1d: Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy...
• 12M.2.sl.TZ2.1e: Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy...
• 12M.2.sl.TZ2.1f: Use your answer to part (e) to calculate the probability that Leanne catches a fish on two...
• 12M.2.sl.TZ2.1g: Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy...
• 11N.2.sl.TZ0.2a: A student is chosen at random from the group. Find the probability that the student (i)    ...
• 11N.2.sl.TZ0.2b: Pam believes that the Mathematics course a student chooses is independent of the language in...
• 09N.1.sl.TZ0.9a: Complete the tree diagram below.
• 09N.1.sl.TZ0.9b: Find the probability that it does not snow tomorrow and Chuck is late for school.
• 09N.1.sl.TZ0.9c: Find the probability that Chuck is late for school.
• 09N.1.sl.TZ0.14a: Draw a Venn diagram in the space below to illustrate this information.
• 09N.1.sl.TZ0.14b: Find the probability that a student studies Spanish given that she studies one language only.
• 11M.1.sl.TZ1.9b: Calculate the probability of rain tomorrow.
• 11M.1.sl.TZ1.9a: Complete the tree diagram below.
• 09M.1.sl.TZ1.11b: Find the probability that the difference between the two numbers shown on the dice is 1.
• 09M.1.sl.TZ1.11c: Find the probability that the number shown on the four-sided die is greater than the number shown...
• 09M.2.sl.TZ1.2i, a: Copy and complete the tree diagram to represent this information.
• 09M.2.sl.TZ1.2i, b: Find the probability that Lisa cooks dinner and they do not have pasta.
• 09M.2.sl.TZ1.2i, d: Given that they do not have pasta, find the probability that Lisa cooked dinner.
• 13M.1.sl.TZ1.5a: Complete the tree diagram below.
• 07M.2.sl.TZ0.5i.b: Neil often takes the dogs to the park after they have eaten. He has noticed that the grey dog...
• 07N.2.sl.TZ0.1i.a: Copy the tree diagram below and fill in all the probabilities, where NL represents not late, to...
• 11M.2.sl.TZ1.2B.a: One of the survey forms was chosen at random, find the probability that the form showed...
• 11M.2.sl.TZ1.2B.b: One of the survey forms was chosen at random, find the probability that the form showed...
• 11M.2.sl.TZ1.2B.c: One of the survey forms was chosen at random, find the probability that the form showed...
• 09M.2.sl.TZ2.1d: A family is chosen at random. Find the probability that they own a cat, given that they own a bird.
• 09M.1.sl.TZ2.10a: If events A and B are mutually exclusive, write down the value of \({\text{P}} (A\cap B)\).
• 09M.1.sl.TZ2.10b: If events A and B are independent, find the value of \({\text{P}} (A\cap B)\).
• 09M.1.sl.TZ2.10c: If \({\text{P}} (A \cup B) = \frac{7}{13}\), find the value of \({\text{P}} (A \cap B)\).
• 09M.1.sl.TZ2.13b: The die is thrown once. Given that the face on top is not red, find the probability that it is...
• 09M.1.sl.TZ2.13c: The die is now thrown twice. Calculate the probability that black appears on top both times.
• 11M.1.sl.TZ2.9a: One traveller is to be chosen at random from all those interviewed. Find the probability that...
• 11M.1.sl.TZ2.9c: One traveller is to be chosen at random from those not going to America. Find the probability...
• 11M.1.sl.TZ2.9b: One female traveller is to be chosen at random from all those interviewed. Find the probability...
• 13M.1.sl.TZ1.5b: Find the probability that Tanay has a sandwich for his lunch.
• 13M.2.sl.TZ1.2d: A student is chosen at random from the 100 that were asked above. Find the probability that this...
• 13M.1.sl.TZ2.10b: Alan returns the sock to the laundry basket and selects two socks at random. Find the...
• 13M.1.sl.TZ2.10c: Alan returns the socks to the laundry basket and again selects two socks at random. Find the...
• 13M.2.sl.TZ2.1c: A family is chosen at random from the group of 40 families. Find the probability that the family...
• 13M.2.sl.TZ2.1d: Two families are chosen at random from the group of 40 families. Find the probability that both...
• SPM.2.sl.TZ0.5c: Tomoko used a bus to travel to school yesterday. Find the probability that she also walked.
• SPM.2.sl.TZ0.5d: Two students are chosen at random from all \(50\) students. Find the probability that(i)    ...
• 07M.2.sl.TZ0.5i.a: One of the dogs is chosen at random. (i) Find P (the dog is grey and has the yellow bowl). (ii)...
• 07M.2.sl.TZ0.5ii.c: Two mice are chosen without replacement. Find P (both mice are short-tailed).
• 07N.2.sl.TZ0.1i.c: Find the probability that Geraldine is late.
• 07N.2.sl.TZ0.1i.d: Find the probability that Geraldine travelled by train, given that she is late.
• 08N.1.sl.TZ0.2d: One student is chosen at random from the group. Find the probability that this student obtained...
• 08N.2.sl.TZ0.3b: Consider the \(200\) drivers surveyed. One driver is chosen at random. Calculate the probability...
• 08N.2.sl.TZ0.3c: Two drivers are chosen at random. Calculate the probability that (i)     both wear a seat...
• 08M.2.sl.TZ1.2i.d: If two students are chosen at random, calculate the probability that they both own a cell phone...
• 08M.2.sl.TZ1.2i.e: If a student owns an iPod, write down the probability that the student also owns a digital camera.
• 08M.2.sl.TZ1.2ii.a: Copy and complete the probability tree diagram below.
• 08M.2.sl.TZ1.2ii.b: Calculate the probability that (i)     Kate goes to the cinema and is not late; (ii)    the...
• 08M.1.sl.TZ2.14a: Complete the tree diagram below.
• 08M.1.sl.TZ2.14b: Find the probability that Andy loses the point.
• 08M.2.sl.TZ2.2i.a: One person is chosen at random from those surveyed. Find the probability that this person (i)...
• 08M.2.sl.TZ2.2i.b: Two people are chosen at random from those surveyed. Find the probability that they both prefer...
• 10M.2.sl.TZ2.1a.ii: Write down the value of b.
• 10M.2.sl.TZ2.1a.iii: Find the probability that both biscuits are plain.
• 10M.2.sl.TZ2.1c.ii: Find the probability that he chooses a biscuit from the red tin given that it is a chocolate...
• 14M.2.sl.TZ2.1a: Find the value of (i)     \({\text{A}}\); (ii)     \({\text{B}}\); (iii)     \({\text{C}}\).
• 14M.2.sl.TZ2.1b: Calculate the probability that Tomek wears (i)     shorts and no tie; (ii)     no tie; (iii)  ...
• 14M.2.sl.TZ2.1c: The conference lasts for two days. Calculate the probability that Tomek wears trousers on both...
• 14M.2.sl.TZ2.1d: The conference lasts for two days. Calculate the probability that Tomek wears trousers on one of...
• 13N.1.sl.TZ0.7a: Complete the tree diagram.
• 13N.1.sl.TZ0.7b: Find the probability that Ramzi buys a magazine when he travels to work.
• 13N.2.sl.TZ0.3e: Find the probability that a woman selected at random from the group had visited Europe.
• 13N.2.sl.TZ0.3f: Find the probability that a woman selected at random from the group had visited Europe, given...
• 13N.2.sl.TZ0.3g: Two women from the group are selected at random. Find the probability that both women selected...
• 14M.1.sl.TZ1.7a: Using the information given, complete the following tree diagram.
• 14M.1.sl.TZ1.7b: Calculate the probability that it will snow tomorrow.
• 14M.2.sl.TZ1.2c: There were 25 tourists in the group and every tourist saw at least one of the three types of...
• 14M.2.sl.TZ1.2d: There were 25 tourists in the group and every tourist saw at least one of the three types of...
• 14N.2.sl.TZ0.2a: Write down the value of (i)     \(p\) ; (ii)     \(q\) ; (iii)     \(r\).
• 14N.2.sl.TZ0.2b: (i)     Find the probability that Mike reaches Trap B. (ii)     Find the probability that Mike...
• 14N.2.sl.TZ0.2c: Sonya, a lab assistant, counts the number of paths that lead to traps or escape doors. She...
• 14N.2.sl.TZ0.2d: During the first trial Mike escapes. Given that Mike escaped, find the probability that he went...
• 15M.1.sl.TZ1.8c: Aleph and Beth are each going to roll their die once only. Shin says the probability that each...
• 15M.1.sl.TZ1.11a: On a day chosen at random, Peter walked to work. Write down the probability that he was on time.
• 15M.1.sl.TZ1.11b: For a different day, also chosen at random, find the probability that Peter cycled to work and...
• 15M.1.sl.TZ1.11c: For a different day, also chosen at random, find the probability that, given Peter was late, he...
• 15M.2.sl.TZ2.1e: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1f: The number of customers that like only mangoes is equal to the number of customers that like only...
• 16M.1.sl.TZ1.1a: The probability that Nikita wins a tennis match depends on the surface of the tennis court on...
• 16M.1.sl.TZ1.1b: Find the probability that Nikita wins a match.
• 16M.2.sl.TZ1.2a: A group of students at Dune Canyon High School were surveyed. They were asked which of the...
• 16M.2.sl.TZ1.2b: Calculate the number of students who were surveyed.
• 16M.2.sl.TZ1.2c: i)     On your Venn diagram, shade the set \({\left( {F \cup M} \right) \cap B'}\) . Do not shade...
• 16M.2.sl.TZ1.2d: A student who was surveyed is chosen at random. Find the probability that (i)     the student...
• 16M.2.sl.TZ1.2e: Dune Canyon High School has 850 students. Find the expected number of students at Dune Canyon...
• 16N.1.sl.TZ0.12a: Complete the tree diagram below.
• 16N.1.sl.TZ0.12b: Find the value of \(p\).
• 16M.1.sl.TZ2.5a: Two friends, Sensen and Cruz, are conducting an investigation on probability. Sensen has a fair...
• 16M.1.sl.TZ2.5b: Find the probability that the number shown on the die is \(1\) or the colour shown on the disc is...
• 16M.1.sl.TZ2.5c: Find the probability that the number shown on the die is even given that the colour shown on the...
• 16N.2.sl.TZ0.2a: Draw a Venn diagram to represent the given information, using sets labelled \(B\), \(C\) and \(H\).
• 16N.2.sl.TZ0.2b: Show that \(x = 3\).
• 16N.2.sl.TZ0.2c: Write down the value of \(n(B \cap C)\).
• 16N.2.sl.TZ0.2d: Find the probability that this person (i)     went on at most one trip; (ii)     went on the...
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 16M.2.sl.TZ2.1a: \(180\) people were interviewed and asked what types of transport they had used in the last year...
• 16M.2.sl.TZ2.1b: Find the number of people who, in the last year, had travelled by (i)      bus only; (ii)  ...
• 16M.2.sl.TZ2.1c: A person is selected at random from those who were interviewed. Find the probability that the...
• 16M.2.sl.TZ2.1d: Given that the person had used only one type of transport in the last year, find the probability...
• 17M.1.sl.TZ1.2a: Calculate the percentage of the population of Ottawa that speak English but not French.
• 17M.1.sl.TZ1.2b: Calculate the number of people in Ottawa that speak both English and French.
• 17M.1.sl.TZ1.2c: Write down your answer to part (b) in the form \(a \times {10^k}\) where...
• 17M.1.sl.TZ1.4a: Write down the number of sporting activities offered by the school during its school year.
• 17M.1.sl.TZ1.4b: Determine whether rock-climbing is offered by the school in the fall/autumn trimester.
• 17M.1.sl.TZ1.4c.i: Write down the elements of the set \(F \cap W’\);
• 17M.1.sl.TZ1.4c.ii: Write down \(n(W \cap S)\).
• 17M.1.sl.TZ1.4d: Write down, in terms of \(F\), \(W\) and \(S\), an expression for the set which contains only...
• 17M.1.sl.TZ1.7a: Complete the tree diagram.
• 17M.1.sl.TZ1.7b: Find the probability that Sara’s baggage arrives in London.
• 17M.1.sl.TZ2.2a: Write down an expression, in terms of \(x\), for the number of children who play only basketball.
• 17M.1.sl.TZ2.2b: Complete the Venn diagram using the above information.
• 17M.1.sl.TZ2.2c: Find the number of children who play only football.
• 17M.1.sl.TZ2.2d: Write down the value of \(n(F)\).
• 17M.1.sl.TZ2.10a: Write down the probability that a light bulb produced by Home Shine is not defective.
• 17M.1.sl.TZ2.10b.i: Find the probability that both light bulbs are not defective.
• 17M.1.sl.TZ2.10b.ii: Find the probability that at least one of Francesco’s light bulbs is defective.
• 17M.1.sl.TZ2.10c: Write down an expression, in terms of \(a\), for the probability that at least one of Deborah’s...
• 17N.1.sl.TZ0.7a: Complete the Venn diagram for these students.
• 17N.1.sl.TZ0.7b: One of the students who joined the sports club is chosen at random. Find the probability that...
• 17N.1.sl.TZ0.7c: Determine whether the events \(S\) and \(M\) are independent.
• 17N.2.sl.TZ0.4a: Find the probability that this person is not allergic to nuts.
• 17N.2.sl.TZ0.4b: Find the probability that both people chosen are not allergic to nuts.
• 17N.2.sl.TZ0.4c: Copy and complete the tree diagram.
• 17N.2.sl.TZ0.4d: Find the probability that this adult is allergic to nuts and the liquid turns blue.
• 17N.2.sl.TZ0.4e: Find the probability that the liquid turns blue.
• 17N.2.sl.TZ0.4f: Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.
• 17N.2.sl.TZ0.4g: Estimate the number of employees, from this 38, who are allergic to nuts.
• 18M.1.sl.TZ1.10a: Complete the Venn diagram using the given information.
• 18M.1.sl.TZ1.10b: Find the value of x.
• 18M.1.sl.TZ1.10c: Write down the value of \(n\left( {\left( {F \cup H} \right) \cap S'} \right)\).
• 18M.2.sl.TZ1.2a: State the alternative hypothesis.
• 18M.2.sl.TZ1.2b: Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.
• 18M.2.sl.TZ1.2c: Write down the number of degrees of freedom.
• 18M.2.sl.TZ1.2d.i: Write down the χ2 statistic.
• 18M.2.sl.TZ1.2d.ii: Write down the associated p-value.
• 18M.2.sl.TZ1.2e: State, with a reason, whether you would reject the null hypothesis.
• 18M.2.sl.TZ1.2f: Write down the probability that this flight arrived on time.
• 18M.2.sl.TZ1.2h: Two flights are chosen at random from those which were slightly delayed. Find the probability...
• 18M.2.sl.TZ1.5a: Write down the probability that Ayako avoids the trap in this wall.
• 18M.2.sl.TZ1.5b: Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to...
• 18M.2.sl.TZ1.5c: Copy the probability tree diagram and write down the relevant probabilities along the branches.
• 18M.2.sl.TZ1.5d.i: A contestant is chosen at random. Find the probability that this contestant fell into a trap...
• 18M.2.sl.TZ1.5d.ii: A contestant is chosen at random. Find the probability that this contestant fell into a trap.
• 18M.2.sl.TZ1.5e: 120 contestants attempted this game. Find the expected number of contestants who fell into a...
• 18M.1.sl.TZ2.7a: State the number of boys who answered questions in Portuguese.
• 18M.1.sl.TZ2.7b: Find the probability that the boy answered questions in Hindi.
• 18M.1.sl.TZ2.7c: Two girls are selected at random. Calculate the probability that one girl answered questions in...
• 18M.2.sl.TZ2.1a.i: Write down the value of a.
• 18M.2.sl.TZ2.1a.ii: Write down the value of b.
• 18M.2.sl.TZ2.1b.i: Use the tree diagram to find the probability that an employee encountered traffic and was late...
• 18M.2.sl.TZ2.1b.ii: Use the tree diagram to find the probability that an employee was late for work.
• 18M.2.sl.TZ2.1b.iii: Use the tree diagram to find the probability that an employee encountered traffic given that they...
• 18M.2.sl.TZ2.1c.i: Find the value of x.
• 18M.2.sl.TZ2.1c.ii: Find the value of y.
• 18M.2.sl.TZ2.1d: Find the number of employees who, in the last year, did not travel to work by car, bicycle or...
• 18M.2.sl.TZ2.1e: Find \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).