Conditional Probability Question..

Question

If one check in 10,000 is forged, 5% of all checks are postdated, and 60% of forged checks are postdated, find the probability that a postdated check is forged.

Answer 1

Let $A$ denote the event that the check is forged and $B$ denote the event that the check is post-dated. You want the probability of a check being forged given that it is post-dated, i.e. $P(A | B)$. By Bayes' rule, $$P(A|B) = \frac{P(A)P(B|A)}{P(B)}.$$ $P(A)$ is the probability that the check is forged. $P(B)$ is the probability that a check is post-dated. $P(B|A)$ is the probability that check is post-dated given that it is forged. You have all these numbers; plug and play.