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If the occurrence of B makes A more likely does the occurrence of A make B more likely?
Wiki User
∙ 13y ago
This is a tricky question, but if you study probability, re-writing it in mathematical notations and using simple definitions and algebra would show you that the answer is yes.
We could rewrite the question as:
if B occur, A is more likely to occur,
Probability of A happening given B happened > probability of A happening
P( A given B) > P(A)
Is it true that in this case, P(B given A) > P(B)?
by definition,
P( B given A) = P(A and B) / P( A) = P( A given B) * P(B) / P(A)
Since P( A given B) > P(A),
then P( A given B)/ P(A) > 1
thus
P( B given A) > P(B)
and the answer is true, occurence of A makes B more likely.
Say A = lung cancer, B = smoking. If someone is smoking, they are more likely to have lung cancer. If someone has lung cancer, they are more likely to be a smoker or have smoked (compared to being a non-smoker).
Wiki User
∙ 13y ago
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