SOLUTION: ii. If P(B)=0.30, P(A│B)=0.60, P(B’)=0.70 and P(A│B’)=0.50, find P(B│A).

Question 1198614: ii. If P(B)=0.30, P(A│B)=0.60, P(B’)=0.70 and P(A│B’)=0.50, find P(B│A).
Answer by ikleyn(52793)   (Show Source): You can put this solution on YOUR website!
.
If P(B)=0.30, P(A│B)=0.60, P(B’)=0.70 and P(A│B’)=0.50, find P(B│A).
~~~~~~~~~~~~~~~~~~~~~~~

        The condition P(B') = 0.7 is excessive in formulation of this problem.
        It follows automatically from the given condition P(B) = 0.30.

From  P(B)=0.30  and  P(A│B)=0.60,  we find  P(A ∩ B)  = 0.30*0.60 = 0.18.

From  P(B')=0.7  and  P(A│B')=0.5,  we find  P(A ∩ B') = 0.50*0.70 = 0.35.



From  P(A ∩ B)  = 0.18  and  P(A ∩ B') = 0.35  we find

      P(A) = P(A ∩ B) + P(A ∩ B') = 0.18 + 0.35 = 0.53.



From  P(A ∩ B) = 0.18  and  P(A) = 0.53  we find

      P(B|A) = P(A ∩ B) / P(A) =  =  = 0.3396  (rounded).    ANSWER

Solved.

RELATED QUESTIONS
If P(A and B) = 0.2 and P (B|A) = 0.5, find P... (answered by math_tutor2020,greenestamps)

4. Compute the probability. a. If P(A) = 0.2 , P(B)= 0.4, and P(A and B) = 0.1, find... (answered by ikleyn)

P(A) = 0.56, P(A and B) = 0.15, find... (answered by Boreal,ikleyn)

If A and B are events with P(A)=0.8, P(A OR B)=0.87, P(A AND B)=0.23, find... (answered by math_tutor2020)

If P(A) > 0, P(B) > 0 and P(A) < P(A|B), show that P(B) < P(B|A) Thank... (answered by ikleyn)

Find the indicated probability. P(A):50% P(B):50% A(A orB)= ______ P(A and B)= 0% (answered by ikleyn)

Suppose P(A)=0.9, P(B)=0.4 and P(B|A)=0.2. What is... (answered by math_tutor2020)

P(A) = 0.31 P(B given A) = 0.8 P(A and B) =... (answered by ikleyn)

P(A) = 0.5 P(B) = 0.6 P(A and B) =... (answered by ikleyn,math_tutor2020)