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IB Mathematics: Applications and Interpretation SL · 13.1: Probability · 13.1.5

Name Date

Combined and mutually exclusive events Problem set A

Write the formula first, then put the numbers in. Give probabilities as decimals or fractions in lowest terms.

Difficulty: first skills applying them stretch

Skills

  1. Find P(A ∩ B) when:

    1. (a) P(A) = 0.55, P(B) = 0.6, P(A ∪ B) = 0.8.
    2. (b) P(A) = 0.45, P(B) = 0.3, P(A ∪ B) = 0.6.

  2. Find P(A ∪ B) when:

    1. (a) P(A) = 0.4, P(B) = 0.35, P(A ∩ B) = 0.15.
    2. (b) P(A) = 0.7, P(B) = 0.45, P(A ∩ B) = 0.3.

  3. Find P(B) when:

    1. (a) P(A) = 0.5, P(A ∩ B) = 0.2, P(A ∪ B) = 0.75.
    2. (b) P(A) = 0.35, P(A ∩ B) = 0.1, P(A ∪ B) = 0.6.

  4. Events A and B are mutually exclusive.

    1. (a) P(A) = 0.28 and P(A ∪ B) = 0.7. Find P(B).
    2. (b) P(A) = 1/6 and P(B) = 3/8. Find P(A ∪ B).

  5. A and B are two events. P(A) = 0.35, P(B) = 0.4 and P(A ∪ B) = 0.7. Are A and B mutually exclusive? Give a reason.

In context

  1. In a town, 34% of households have a cat, 27% have a dog and 9% have both. A household is chosen at random.

    1. (a) Find the probability that the household has a cat or a dog (or both).
    2. (b) Find the probability that the household has neither.

  2. At a school, a student is chosen at random. The probability that the student plays netball is 0.46, and the probability that the student plays hockey is 0.38. The probability that the student plays netball or hockey (or both) is 0.7.

    1. (a) Find the probability that the student plays both sports.
    2. (b) Find the probability that the student plays netball but not hockey.

  3. A commuter chooses one way to travel to work. The probability of cycling is 0.34 and the probability of taking the train is 0.41. The two are mutually exclusive.

    1. (a) Find the probability that the commuter cycles or takes the train.
    2. (b) Find the probability that the commuter does neither.

  4. At a college, 52% of students do swimming, 38% do chess and 15% do both. A student is chosen at random.

    1. (a) Find the probability that the student does exactly one of the two activities.
    2. (b) Find the probability that the student does neither.

Stretch

  1. A and B are mutually exclusive events with \(P(A)=x\), \(P(B)=2x+0.06\) and \(P(A\cup B)=0.69\).

    1. (a) Write an equation for x and solve it.
    2. (b) Find P(A) and P(B).

  2. A student at a school is chosen at random. The Venn diagram shows probabilities for A, the student takes art, and B, the student takes music.

    0.320.18y0.25AB
    1. (a) Find the value of y.
    2. (b) Find P(B).
    3. (c) Use P(A) + P(B) − P(A ∩ B) to find P(A ∪ B), and check it against the regions inside the circles.

jmaths.xyz · AI SL · 13.1.5 Combined events and mutually exclusive events