Conditional probability and independence

Conditional probability and independence Quiz

Spec 3.2–3 · Edexcel International A Level Maths: Quiz

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5 questions, one answer each

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  1. 1. P(A)=0.6P(A)=0.6 and P(A∩B)=0.3P(A\cap B)=0.3. Find P(B∣A)P(B\mid A).

    • A. 0.180.18
    • B. 0.90.9
    • C. 0.50.5
    • D. 0.30.3

  2. 2. AA and BB are independent, P(A)=0.4P(A)=0.4 and P(B)=0.5P(B)=0.5. Find P(A∩B)P(A\cap B).

    • A. 0.90.9
    • B. 0.10.1
    • C. 0.50.5
    • D. 0.20.2

  3. 3. Which statement is true for independent events AA and BB?

    • A. P(B∣A)=P(B)P(B\mid A)=P(B)
    • B. P(A∩B)=0P(A\cap B)=0
    • C. P(A∪B)=P(A)+P(B)P(A\cup B)=P(A)+P(B)
    • D. P(A)=P(B)P(A)=P(B)

  4. 4. A bag has 4 red and 6 green counters. Two are drawn without replacement. Find the probability that both are red.

    • A. 425\frac{4}{25}
    • B. 215\frac{2}{15}
    • C. 25\frac25
    • D. 310\frac{3}{10}

  5. 5. P(A)=0.5P(A)=0.5, P(B)=0.2P(B)=0.2 and P(A∩B)=0.1P(A\cap B)=0.1. What can you conclude?

    • A. The events are mutually exclusive.
    • B. The events are not independent because P(A)≠P(B)P(A)\neq P(B).
    • C. The events are not independent because P(A∩B)≠0P(A\cap B)\neq0.
    • D. The events are independent because P(A)P(B)=P(A∩B)P(A)P(B)=P(A\cap B).

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