Question

Consider randomly selecting a single individual and having that person test drive different vehicles. Define events , , and by Suppose that , , , , , and . What is the probability that the individual likes both vehicle

Answer 1

`P(A_1\ n\ A_2) = 0.40`

Explanation:

Let:

`A_1 \to` An Individual likes vehicle 1

`A_2 \to` An Individual like vehicle 2

`P(A_1) = 0.55`

`P(A_2) = 0.65`

`P (A_1\ u\ A_2 ) = 0.80`

Required

`P(A_1\ n\ A_2)` --- probability that both vehicles are liked by the individual.

This is calculated as:

`P(A_1\ n\ A_2) = P(A_1) + P(A_2) - P(A_1\ u\ A_2)`

So, we have:

`P(A_1\ n\ A_2) = 0.55 + 0.65 - 0.80`

`P(A_1\ n\ A_2) = 0.40`