SOLUTION: If ​P(B)equals 0.2​, ​P(A | ​B)equals 0.5​, ​P(Upper B prime​)equals 0.8​, and​ P(A | Upper B prime​)equals 0.7​, find​ P(B |​ A).

Algebra ->  Probability-and-statistics -> SOLUTION: If ​P(B)equals 0.2​, ​P(A | ​B)equals 0.5​, ​P(Upper B prime​)equals 0.8​, and​ P(A | Upper B prime​)equals 0.7​, find​ P(B |​ A).      Log On


   

Question 1137147: If ​P(B)equals 0.2​, ​P(A | ​B)equals 0.5​, ​P(Upper B prime​)equals 0.8​, and​ P(A | Upper B prime​)equals 0.7​, find​ P(B |​ A).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Given info:
P(B) = 0.2
P(A|B) = 0.5
P(B') = 0.8
P(A|B') = 0.7

Through the law of total probability, we can say,
P(A) = P(A|B)*P(B) + P(A|B')*P(B')
P(A) = 0.5*0.2 + 0.7*0.8
P(A) = 0.66

Now use Bayes Theorem to get the conditional probability we want








The approximate answer, accurate to four decimal places, is 0.1515