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

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Conditional probability Problem set B

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).

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. A box holds 7 chocolates and 5 mints. Two sweets are taken out at random, one after the other, without replacement. The first sweet is a mint.

    1. (a) Find the probability that the second sweet is a mint.
    2. (b) Find the probability that the second sweet is a chocolate.

  2. A game uses 36 cards: four suits of nine cards, numbered 1 to 9. Two cards are taken at random, without replacement. The first card is the 7 of hearts.

    1. (a) Find the probability that the second card is a heart.
    2. (b) Find the probability that the second card is a 7.

  3. The table shows the type of film and the age group of the people in a cinema one evening.

    FilmUnder 1818 or overComedy2431Thriller933Cartoon2815
    1. (a) Find the probability that a person chosen at random is under 18, given that the person watches a thriller.
    2. (b) Find the probability that a person chosen at random watches a cartoon, given that the person is 18 or over.

  4. In a group of 80 members of a club, 44 cycle to the club, 30 come by bus and 14 do both on different days. Let C be the set who cycle and B the set who come by bus. Draw a Venn diagram.

    1. (a) Find the probability that a member comes by bus, given that the member cycles.
    2. (b) Find the probability that a member cycles, given that the member does not come by bus.

  5. The Venn diagram shows how 50 children use R, the roller rink, and G, the games room.

    1781213RG
    1. (a) Find the probability that a child uses the games room, given that the child uses the rink.
    2. (b) Find the probability that a child uses neither, given that the child does not use the rink.

In context

  1. A survey of 90 teenagers found that 50 own a bike, 35 own a scooter and 15 own both. Let B be the set who own a bike and S the set who own a scooter.

    1. (a) Find the probability that a teenager owns a scooter, given that the teenager owns a bike.
    2. (b) Find the probability that a teenager owns a bike, given that the teenager owns no scooter.

  2. A customer at a café is chosen at random. The probability that the customer buys a drink but no food is 0.24. The probability that the customer buys both is 0.18. The probability that the customer buys neither is 0.36.

    1. (a) Find the probability that the customer buys food, given that the customer buys a drink.
    2. (b) Find the probability that the customer buys a drink, given that the customer buys food.

Stretch

  1. A drawer holds 6 grey, 3 white and 2 black socks. Two socks are taken out at random, one after the other, without replacement.

    1. (a) Given that the first sock is white, find the probability that the second sock is not white.
    2. (b) Find the probability that both socks are grey.

  2. At a leisure centre, A is the event that a visitor swims and B is the event that the visitor uses the gym. P(A) = 0.7, P(B) = 0.5 and P(A ∪ B) = 0.85.

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

jmaths.xyz · AI SL · 13.1.6 Conditional probability