Answer to Question #15608 in Statistics and Probability for abid khan
P(A|B) = P(B|A)*P(A)/P(B).
Here by A and B we denoted the following events:
event A - cereal box is winner
event B - cereal box rattles
One box in a million is a winner, so
P(A) = 10^(-6).
1% of all boxes rattle, so
P(B) = 10^(-2).
All of winning boxes rattles, so
P(B|A) = 1.
P(A|B) = P(B|A)*P(A)/P(B) = 1*10^(-6)/10^(-2) = 10^(-4).
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