SOLUTION: Given P(A|B) = .7 , and P(B|A) = .6 , which is larger, P(A) or P(B)? Show work .

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Question 924353: Given P(A|B) = .7 , and P(B|A) = .6 , which is larger, P(A) or P(B)? Show work .
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
p(a|b) = p(ab) / p(b)

p(b|a) = p(ab) / p(a)

you know what p(a|b) is and you know what p(b|a) is.

you also know that p(ab) is the same in either equation.

let x = p(ab) and replace p(a|b) with .7 and replace p(b|a) with .6 and you get:

.7 = x/p(b)

.6 = x/p(a)

solve for p(b) in the first equation to get p(b) = x/.7

solve for p(a) in the second equation to get p(a) = x/.6

since x/.6 is bigger than x/.7, p(a) must be bigger.