## Using Bayes' theorem gives a probability > 1. [closed]

I am probably misusing Bayes' theorem, but I can't figure out how.

P(B|A) = 0.4

P(B) = 0.1

P(A) = 0.3

P(A|B) = 0.4 * 0.3 / 0.1 = 1.2

This just says the hypothesis is nonsense. $P(B|A) = P(A\cap B) / P(A)$. But $P(A\cap B) \leq P(B)$. So your assumption would imply that $0.4 \leq 0.1 / 0.3$ which is nonsensical. In words, if A happens thrice out of ten and when A happens, B happens 4 times out of ten, you must have that B happens at least, over all, 12 times out of 100, which is incompatible with you assumption that B only happens once in ten. – Willie Wong Jun 17 2011 at 22:06