单选题 The probability of A is 0.4. The probability of A^C is 0.6. The probability of (B|A) is 0.5, and the probability of ( B| A^C) is 0.2. Using Bayes' formula, what is the probability of ( A|B) ?

A. 0.625.
B. 0.875.
C. 0.125.

A
B
C
D

【正确答案】 A

【答案解析】Using the total probability rule, we can compute the P(B) :
P(B) =[P(B|A) ×P(A)] +[P(B|A^C)×P(A^C) ]
P(B) = [0.5×0.4] + [0.2×0.6] =0.32
Using Bayes' formula, we can solve for P(A|B) :
P(A|B) =[ P(B|A)/P(B) ] ×P(A) =[0.5/0.321×0.4=0.625