Question

The probability that a mechanical issue is reported on a rental van during the rental period is 0.25. A rental company rents out two vans on a particular day. Assume that mechanical issues emerge independently of each other (so that it’s not some mechanic’s fault).

Determine the following probabilities and show all your work.

1. What is the probability that both vans will require repairs during the rental period?

2. What is the probability that exactly one van will require repairs during the rental period?

3. What is the probability that neither van will require repairs during the rental period?

Answer 1

The probability that both vans will require repairs is 0.0625. The probability that exactly one van will require repairs is 0.1875. The probability that neither van will require repairs is 0.5625.

Step-by-step explanation:

To solve this problem, we will use the concept of independent events and the multiplication rule of probability.

1. What is the probability that both vans will require repairs during the rental period?

The probability of one van requiring repairs is 0.25, so the probability of both vans requiring repairs is 0.25 * 0.25 = 0.0625.

2. What is the probability that exactly one van will require repairs during the rental period?

The probability of one van requiring repairs is 0.25, and the probability of the other van not requiring repairs is 0.75. Since the events are independent, the probability of exactly one van requiring repairs is 0.25 * 0.75 = 0.1875.

3. What is the probability that neither van will require repairs during the rental period?

The probability of one van not requiring repairs is 0.75, so the probability of neither van requiring repairs is 0.75 * 0.75 = 0.5625