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I have a question on a review that I just cannot crack.
It goes as follows:
"Event A occurs with probability .4. The conditional probability that A occurs given B occurs is .5, while the probability that A occurs given that B does not occur is .2. What is the conditional Probability that B occurs given A occurs."
P(A) = .4
P(A|Not B) = .2.
I've tried multiplying things out. I just can't get it .
Can anyone help?
From the given data you have:
Pr(A | B) = 1/2 => a/(a + b) = 1/2 => a = b .... (1)
Pr(A | B') = 1/5 => c/(c + d) = 1/5 => d = 4c .... (2)
a + c = 2/5 ..... (3)
b + d = 3/5 .... (4)
Solve equations (1), (2), (3) and (4) simultaneously for a, b, c and d and complete the above table. The answer to your question is Pr(B | A) = a/0.4 = 5a/2.
I get Pr(B | A) = 5/6.