Suppose that PAB04 PAB02 and PB08 Determine PBASolutionGiven

Suppose that P(A/B)=0.4, P(A/B\')=0.2, and P(B)=0.8 Determine P(B/A)?

Solution

Given P(A/B)=0.4

--> P(A and B)/ P(B) = 0.4

--> P(A and B) / 0.8 =0.4

--> P(A and B) = 0.4*0.8 =0.32

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Given P(A/B\')=0.2

--> P(A and B\') / P(B\') =0.2

--> P(A and B\')/ (1-P(B)) = 0.2

--> P(A and B\') /(1-0.8) = 0.2

--> P(A and B\') =0.2*0.2 =0.04

--> P(A) - P(A and B) =0.04

--> P(A) -0.32 = 0.04

--> P(A) =0.32 +0.04 =0.36

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So P(B/A) = P(A and B)/P(A)

=0.32/0.36

=0.8889