Question

The probability that Michael misses a free throw shot is .1. If he goes to the line to shoot three free throws (due to a foul on a three-point shot), (pjs) a) What is the probability that Michael misses all three shots? What assumptions did you make in order to calculate this probability?

Answer 1

To calculate the probability that Michael misses all three shots, you can multiply the probabilities of each individual shot. This assumes that each free throw shot is independent of the others.

Step-by-step explanation:

To calculate the probability that Michael misses all three shots, we can multiply the probabilities of each individual shot. Since the probability of missing a free throw shot is 0.1, the probability of missing all three shots is 0.1 * 0.1 * 0.1 = 0.001.

The assumption made in calculating this probability is that each free throw shot is independent of the others. That is, the outcome of one shot does not affect the outcome of the others. This assumption allows us to simply multiply the probabilities together.

Answer 2

1) The probability that Michael misses all three free throws is
`\(0.1^3 = 0.001\)`.

2) This is calculated by multiplying the individual probabilities of missing each free throw.

Step-by-step explanation:

1) The probability of missing a single free throw is given as 0.1. To find the probability of missing all three free throws, we raise this probability to the power of 3 (since there are three independent events):
`\(0.1^3 = 0.001\).`

2) This calculation assumes that each free throw is independent, meaning the outcome of one does not affect the outcome of another. In this context, it implies that Michael's performance on one free throw does not impact his performance on subsequent ones.