DP Mathematical Studies Questionbank

• Syllabus

3.7

Sub sections and their related questions

Probability of combined events, mutually exclusive events, independent events.

• 10M.1.sl.TZ1.8b: Find the probability that Maria is late for school.
• 10M.1.sl.TZ1.13b: Find the probability that a student chosen at random is either male or studies Chemistry.
• 10M.1.sl.TZ2.8a: Find \({\text{P}}(A \cap B)\).
• 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.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.TZ1.12b: Find the probability that Merryn will not be late for the concert.
• 10M.2.sl.TZ2.1c.i: Find the probability that he chooses a chocolate biscuit.
• 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.TZ2.1d: 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...
• 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.TZ0.9b: 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.
• 11M.1.sl.TZ1.9b: Calculate the probability of rain tomorrow.
• 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, b: Find the probability that Lisa cooks dinner and they do not have pasta.
• 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...
• 11M.2.sl.TZ1.2B.b: One of the survey forms was chosen at random, find the probability that the form showed...
• 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.TZ2.13c: 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.TZ2.9b: 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...
• 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.
• 08N.1.sl.TZ0.2d: One student is chosen at random from the group. Find the probability that this student obtained...
• 08N.2.sl.TZ0.3c: 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.TZ1.2ii.b: Calculate the probability that (i)     Kate goes to the cinema and is not late; (ii)    the...
• 08M.1.sl.TZ2.14b: Find the probability that Andy loses the point.
• 08M.2.sl.TZ2.2i.b: Two people are chosen at random from those surveyed. Find the probability that they both prefer...
• 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.TZ0.7b: 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.TZ0.3g: Two women from the group are selected at random. Find the probability that both women selected...
• 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...
• 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.TZ1.11b: For a different day, also chosen at random, find the probability that Peter cycled to work and...
• 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...
• 16N.1.sl.TZ0.12b: Find the value of \(p\).
• 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 \(A\).
• 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.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.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 \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).

Use of tree diagrams, Venn diagrams, sample space diagrams and tables of outcomes.

• 10M.1.sl.TZ1.8a: Complete the tree diagram below, showing the appropriate probabilities.
• 10M.1.sl.TZ1.13a: Find the probability that a student chosen at random is male.
• 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.
• 12M.1.sl.TZ1.12a: Complete the tree diagram below.
• 10M.2.sl.TZ2.1a.i: Write down the value of a.
• 10M.2.sl.TZ2.1b: Copy and complete the tree diagram below.
• 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...
• 09N.1.sl.TZ0.9a: Complete the tree diagram below.
• 11M.1.sl.TZ1.9a: Complete the tree diagram below.
• 09M.2.sl.TZ1.2i, a: Copy and complete the tree diagram to represent this information.
• 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...
• 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.2.sl.TZ1.2d: A student is chosen at random from the 100 that were asked above. Find the probability that this...
• 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...
• 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.TZ1.2ii.a: Copy and complete the probability tree diagram below.
• 08M.1.sl.TZ2.14a: Complete the tree diagram below.
• 10M.2.sl.TZ2.1a.ii: Write down the value of b.
• 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.
• 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...
• 16N.1.sl.TZ0.12b: Find the value of \(p\).
• 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.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 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.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 using “with replacement” and “without replacement”.

• 10M.2.sl.TZ2.1a.i: Write down the value of a.
• 10M.2.sl.TZ2.1c.i: Find the probability that he chooses a chocolate biscuit.
• 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...
• 07M.2.sl.TZ0.5ii.c: Two mice are chosen without replacement. Find P (both mice are short-tailed).
• 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.
• 15M.2.sl.TZ2.1f: The number of customers that like only mangoes is equal to the number of customers that like only...
• 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 \(A\).
• 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 \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).

Conditional probability.

• 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.TZ2.8b: Find \({\text{P}}(A|B)\).
• 11N.1.sl.TZ0.10a: Write down the probability that (i) Ju Shen chooses a red disc from the bag; (ii) Ramón chooses...
• 10N.1.sl.TZ0.6b: Write down the probability that this person is male given that they are a smoker.
• 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.TZ1.12c: Merryn was not late for the concert the next day. Given that, find the probability that she...
• 12M.2.sl.TZ2.1b: Leanne catches a fish. Find the probability that she (i) catches an undersized bream; (ii)...
• 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)    ...
• 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.
• 09M.2.sl.TZ1.2i, d: Given that they do not have pasta, find the probability that Lisa cooked dinner.
• 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...
• 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.TZ2.13b: The die is thrown once. Given that the face on top is not red, find the probability that it is...
• 11M.1.sl.TZ2.9c: One traveller is to be chosen at random from those not going to America. Find the probability...
• 13M.2.sl.TZ1.2d: A student is chosen at random from the 100 that were asked above. Find the probability that this...
• 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.
• 07N.2.sl.TZ0.1i.d: Find the probability that Geraldine travelled by train, given that she is late.
• 08N.2.sl.TZ0.3b: Consider the \(200\) drivers surveyed. One driver is chosen at random. Calculate the probability...
• 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.TZ2.2i.a: One person is chosen at random from those surveyed. Find the probability that this person (i)...
• 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.TZ2.1b: Calculate the probability that Tomek wears (i)     shorts and no tie; (ii)     no tie; (iii)  ...
• 13N.2.sl.TZ0.3f: Find the probability that a woman selected at random from the group had visited Europe, given...
• 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.TZ0.2d: During the first trial Mike escapes. Given that Mike escaped, find the probability that he went...
• 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...
• 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 \(A\).
• 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...
• 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.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 \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).