Question
Asked Dec 1, 2019
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Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. 

P(A | B) = .4, P(B) = .9, P(A | B') = .8. Find P(B | A).

P(B | A) = 

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Expert Answer

Step 1

Given that

P (A/B) = 0.4

P (B) = 0.9

P (A/B’) = 0.8

P (B/A) =?

Step 2

According to Bayes’ theorem, they defined that

P(A/B)P(B)
P(A)
P(B/A)
wewant to find P(A), use the law of total probability
P(A) P(A B)P(B) + P(A/ B')P(B ')
and
P(B')1-P(B)
help_outline

Image Transcriptionclose

P(A/B)P(B) P(A) P(B/A) wewant to find P(A), use the law of total probability P(A) P(A B)P(B) + P(A/ B')P(B ') and P(B')1-P(B)

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Step 3

Substitute the...

P(B') 1-P(B)
1-0.9
= 0.1
P(A) P(AIB)P(B) + P(A / B')P (B')
=0.4(0.9)+0.8(0.1)
=0.36 0.08
P(A) 0.44
help_outline

Image Transcriptionclose

P(B') 1-P(B) 1-0.9 = 0.1 P(A) P(AIB)P(B) + P(A / B')P (B') =0.4(0.9)+0.8(0.1) =0.36 0.08 P(A) 0.44

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