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Question

Let A and B be independent events with P(A)=0.3 and P(B)=0.4. Find
(i) P(AB)
(ii) P(AB)
(iii) P(A|B)
(iv) P(B|A)

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Solution

It is given that P(A)=0.3 and P(B)=0.4
(i) If A and B are independent events, then
P(AB)=P(A)P(B)=0.3×0.4=0.12
(ii) It is known that, P(AB)=P(A)+P(B)P(AB)
P(AB)=0.3+0.40.12=0.58
(iii) It is known that, P(A|B)=P(AB)P(B)
P(A|B)=0.120.4=0.3
(iv) It is known that, P(B|A)=P(AB)P(A)
P(B|A)=0.120.3=0.4

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