Question

If P(B)= 0.15, P(A|B)=0.40, P(B')=0.85, and P(A|B')=0.70, find P(B|A)

Answer 1

Answer :-

(If we round answer up to 2 decimal places)

Or

(Without round answer)

The complete solution of above question are as below

If P(B)= 0.15, P(A|B)=0.40, P(B')=0.85, and P(A|B')=0.70

We have to find P(B|A) using following formula

P(B|A) = P(AB)/P(A)

First we find the P(AB) & P(A) values

P(A|B)=0.40

P(A|B)= P(AB)/P(B) = 0.40

P(AB)/0.15 = 0.40

P(AB) = 0.15 * 0.40 = 0.06

P(AB) = 0.06 ---------(1)

P(A|B')=0.70

Which is also written using following formula

  

We have to find P(B|A) using following formula

(Without round answer)

Or

If you have need to answer up to 2 decimal places then it is as below

(Round answer up to 2 decimal places)

Summary :-

(If we round answer up to 2 decimal places)

Or

(Without round answer)