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IB Mathematics: Applications and Interpretation SL · 13.1: Probability · 13.1.6

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Conditional probability Problem set A

Say which outcomes are left after the 'given that', then divide. Give each probability as a fraction in lowest terms (a decimal too if it is exact).

Difficulty: first skills applying them stretch

Skills

  1. A bag contains 9 yellow counters and 6 green counters. Two counters are taken out at random, one after the other, without replacement. The first counter is yellow.

    1. (a) Find the probability that the second counter is yellow.
    2. (b) Find the probability that the second counter is green.

  2. Two cards are taken at random from a standard pack of 52 cards, without replacement. The first card is the ace of clubs.

    1. (a) Find the probability that the second card is a club.
    2. (b) Find the probability that the second card is an ace.

  3. The table shows the subject chosen and the gender of the students in a sixth form.

    SubjectGirlsBoysBiology2718History1221Art166
    1. (a) Find the probability that a student chosen at random is a girl, given that the student takes biology.
    2. (b) Find the probability that a student chosen at random takes art, given that the student is a boy.

  4. In a group of 60 students, 35 play netball, 28 play hockey and 12 play both. Let N be the set who play netball and H the set who play hockey. Draw a Venn diagram.

    1. (a) Find the probability that a student plays hockey, given that the student plays netball.
    2. (b) Find the probability that a student plays netball, given that the student does not play hockey.

  5. The Venn diagram shows how 40 members of a club use T, the tennis courts, and S, the squash courts.

    141196TS
    1. (a) Find the probability that a member uses squash, given that the member uses tennis.
    2. (b) Find the probability that a member uses neither, given that the member does not use tennis.

In context

  1. A survey of 120 households found that 66 have a garden, 48 have a pet and 30 have both. Let G be the set with a garden and P the set with a pet.

    1. (a) Find the probability that a household has a pet, given that it has a garden.
    2. (b) Find the probability that a household has a garden, given that it has no pet.

  2. A student at a college is chosen at random. The probability that the student runs but does not swim is 0.30. The probability that the student runs and swims is 0.15. The probability that the student does neither is 0.30.

    1. (a) Find the probability that the student swims, given that the student runs.
    2. (b) Find the probability that the student runs, given that the student swims.

Stretch

  1. A bag holds 5 red, 4 blue and 3 green counters. Two counters are taken out at random, one after the other, without replacement.

    1. (a) Given that the first counter is blue, find the probability that the second counter is not blue.
    2. (b) Find the probability that both counters are red.

  2. In a village, A is the event that a household has broadband and B is the event that it has a landline. P(A) = 0.5, P(B) = 0.4 and P(A ∪ B) = 0.65.

    1. (a) Find P(A ∩ B).
    2. (b) Find P(A | B).

jmaths.xyz · AI SL · 13.1.6 Conditional probability