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4.4.1 Probability (A-level only)

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Question 12

The events A A\,A and B B\,B are such that P(A)=0.45P(A) = 0.45P(A)=0.45, P(B)=0.6P(B) = 0.6P(B)=0.6 and P(A∣B)=13\displaystyle P(A|B) = \frac{1}{3}P(A∣B)=31​.

a.

Find P(A∩B)P(A \cap B)P(A∩B).

[2]
b.

Find P(B′∣A)P(B'|A)P(B′∣A).

[3]
c.

Find P(A′∪B)P(A' \cup B)P(A′∪B).

[2]
d.

Determine whether the events A A\,A and B B\,B are independent, give a reason for your answer.

[3]

4.4.1 Probability (A-level only) Questions

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