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Question

Let A and B be independent events with P(A)=0.2,P(B)=0.5. Then find:
(i) P(A|B)
(ii) P(B|A)
(iii) P(AB)
(iv) P(AB)

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Solution

If A and B are independent events then P(AB)=P(A)P(B)=0.2×0.5=0.1
Therefore,
(i) P(A|B)=P(AB)P(B)=P(A)P(B)P(B)=P(A)=0.2
(ii) P(B|A)=P(AB)P(A)=P(A)P(B)P(A)=P(B)=0.5
(iii) P(AB)=0.1
(iv) P(AB)=P(A)+P(B)P(AB)=0.2+0.50.1=0.6

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