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).
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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) (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
 = \frac{P(A|B)*P(B)}{P(A)})
 = \frac{0.5*0.2}{0.66})
 = \frac{0.1}{0.66})
 \approx 0.1515)
The approximate answer, accurate to four decimal places, is 0.1515
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