Question

A candidate runs for two political offices, A and B. He assigns 0.30 as the probability of being elected to both, 0.6 as the probability of being elected to A if he is elected to B and 0.8 as the probability of being elected to B if he is elected to A. What is the probability of being elected to A?

Answer 1

$P(A|B) = 0.6 \\ P(B|A) = 0.8 \\ P(A \cap B) = 0.30 \\ P(B|A) = \frac{P(B \cap A)}{P(A)} \\ P(A) = \frac{P(B \cap A)}{P(B|A)} \\ P(A) = \frac{0.30}{0.80} = 0.375$