Question

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

Answer 1

Let $A$ denotes the event that a person has seen the commercial and $B$ denotes the event that a person has bought the product.

Given $P(A)=0.3, P(B)=0.2$

$$P(AB)=P(A)P(B)=0.3(0.2)=0.06$$

The probability that a person chosen at random in the country, will have seen the commercial and bought the product is $0.06.$