If A and B are events in an outcome space omega and we know

If A and B are events in an outcome space (omega) and we know that P(A)=0.43, P(B|A)=.65, and P (A U B)=.52, what is P(B)?

Solution

Given that P(A)=0.43, P(B|A)=.65

But P(B/A) = P(AB)/P(A) =0.65

Hence P(AB) = 0.65(0.43) = 0.2795

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Consider P(AUB)

= P(A)+P(B)-P(AB)

i.e. 0.52 = 0.43+P(B)-0.2795

P(B) = 0.52+0.2795-0.43

= 0.3695