DP Mathematical Studies Questionbank

• Syllabus

3.6

Sub sections and their related questions

Sample space; event $A$; complementary event, ${A'}$ .

• 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...
• 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)...
• 08M.2.sl.TZ2.2i.a: One person is chosen at random from those surveyed. Find the probability that this person (i)...
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of $r$ which minimizes $A$.
• 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 $n\left( {\left( {C \cup B} \right) \cap P'} \right)$.

Probability of an event.

• 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)...
• 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.
• 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...
• 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.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.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.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of $r$ which minimizes $A$.
• 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 $n\left( {\left( {C \cup B} \right) \cap P'} \right)$.

Probability of a complementary event.

• 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...
• 09M.2.sl.TZ1.2i, c: Find the probability that they do not have pasta.
• 08N.2.sl.TZ0.3b: Consider the $200$ drivers surveyed. One driver is chosen at random. Calculate the probability...
• 08M.2.sl.TZ1.2ii.b: Calculate the probability that (i)     Kate goes to the cinema and is not late; (ii)    the...
• 14M.2.sl.TZ2.1a: Find the value of (i)     ${\text{A}}$; (ii)     ${\text{B}}$; (iii)     ${\text{C}}$.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of $r$ which minimizes $A$.
• 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 $n\left( {\left( {C \cup B} \right) \cap P'} \right)$.

Expected value.

• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of $r$ which minimizes $A$.
• 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 $n\left( {\left( {C \cup B} \right) \cap P'} \right)$.