Question 1137147
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Given info:
P(B) = 0.2
P(A|B) = 0.5
P(B') = 0.8
P(A|B') = 0.7


Through the <a href = "https://en.wikipedia.org/wiki/Law_of_total_probability">law of total probability</a>, 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 <a href = "https://en.wikipedia.org/wiki/Bayes%27_theorem">Bayes Theorem</a> to get the conditional probability we want
*[Tex \Large P(B|A) = \frac{P(A|B)*P(B)}{P(A)}]


*[Tex \Large P(B|A) = \frac{0.5*0.2}{0.66}]


*[Tex \Large P(B|A) = \frac{0.1}{0.66}]


*[Tex \Large P(B|A) \approx 0.1515]


The approximate answer, accurate to four decimal places, is <font size=4 color=red>0.1515</font>
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