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IB Mathematics: Applications and Interpretation HL · 13.1: Probability · 13.1.2

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Venn diagrams for probability Problem set B

Draw a Venn diagram for each question and put the overlap in first. Give probabilities as fractions in lowest terms unless the question asks for a decimal.

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. Of 60 staff at a college, 34 drive to work and 28 cycle to work. 12 do both, on different days. One member of staff is chosen at random. Find the probability that the person

    1. (a) drives but does not cycle.
    2. (b) cycles but does not drive.

  2. At a youth club of 45 members, 27 like chess and 20 like draughts. 9 like both games. Find the probability that a member chosen at random likes neither game.

  3. The Venn diagram shows the 60 children at a holiday camp. R is the set who go riding and H is the set who go hiking. The numbers are numbers of children. A child is chosen at random. Find the probability that the child

    1921812RH
    1. (a) goes riding.
    2. (b) goes riding but does not go hiking.
    3. (c) is in neither set.

  4. In a sixth form of 110 students, 18 study both Physics and Chemistry, 25 study neither subject and 40 study Physics only.

    1. (a) How many students study Chemistry only?
    2. (b) A student is chosen at random. Find the probability that the student studies Chemistry.

In context

  1. A poll asks 150 voters which newspapers they read. 84 read a daily paper, 65 read a weekly paper and 31 read both.

    1. (a) Draw a Venn diagram.
    2. (b) Find the probability that a person chosen at random does neither.
    3. (c) Find the probability that a person chosen at random does exactly one.

  2. Of 240 customers at a stall, 42 buy both tea and coffee, 30 buy neither and 95 buy coffee only. A customer is chosen at random. Find the probability that the customer buys tea. Give your answer as a decimal.

Stretch

  1. At a sports centre, the probability that a member swims is 0.7 and the probability that a member plays squash is 0.45. The probability that a member does neither is 0.05.

    1. (a) Find the probability of a member doing both.
    2. (b) Find the probability of a member swimming but not playing squash.

  2. In a group of 90 players, 16 play both tennis and badminton and 14 play neither. The number who play tennis only is 6 more than the number who play badminton only. Find the probability that a player chosen at random plays badminton. Give your answer as a fraction.

jmaths.xyz · AI HL · 13.1.2 Venn diagrams for probability