Answer to Question #236659 in Statistics and Probability for Steve

Question

A company estimates that 30% of the country has seen its commercial and that if a person
is the probability that a person chosen at random in the country will have seen the
sees its commercial, there is a 20% probability that the person willbuy its product. What
commercial and bought the product?

Answer 1

$P(buys|seen) = 0.2 \\ P(seen) = 0.3 \\ P(A \cap B) = P(B) \times P(A|B)$

For independent events

$P(A \cap B) = P(B) \times P(A) \\ P(buys \cap seen) = P(seen) \times P(buys|seen) \\ = 0.3 \times 0.2 \\ = 0.06$