Question

55. Multiply probabilities? In a recent year, 21% of all vehicles in operation were pickup trucks. If someone owns two vehicles, is the probability that they are both pickup trucks equal to 0.21 x 0.21 = 0.0441? Explain why or why not.

Answer 1

The probability that both vehicles owned by a person are pickup trucks is indeed 0.0441 under the assumption that the events are independent, meaning one does not affect the probability of the other.

Step-by-step explanation:

The probability that someone owns two vehicles and they are both pickup trucks, given that 21% of all vehicles in operation were pickup trucks, can indeed be calculated by multiplying the individual probabilities if we assume the events are independent.

The assumption of independence implies that the probability of one vehicle being a pickup truck does not affect the probability of the second vehicle being a pickup truck.

In mathematical terms, the probability that both vehicles are pickup trucks is

P(A and B) = P(A) × P(B)

= 0.21 × 0.21

= 0.0441.

However, this is only accurate if there is no connection between the ownership of the first and second vehicle being a pickup truck.