Question

Suppose P(C|D)=0.59, P(D)=0.44, and P( D|C)=0.38. What is P(C) rounded to two decimal places?

Answer 1

From the information given.
P(CΙD) = P(C∩D)/P(D)
P(DΙC) = P(C∩D)/P(C)
Therefore;
P(C∩D) = P(CΙD) × P(D)= P(DΙC) ×P(C)
P(C∩D)= 0.59×0.44
             = 0.2596
P(C) = P(C∩D)/P(DΙC)
        =  0.2596/0.38
        = 0.68316
        ≈ 0.68