Question

A basketball player gets 2 free throw shots when she is fouled by another player on the opposing team. She misses the first shot 40% of the time. When she misses the first shot, she misses the second shot 5% of the time. What is the probability of missing both free throw shots?

Answer 1

The probability of missing both free throw shots is calculated by multiplying the probability of missing the first shot by the probability of missing the second shot, given the first is missed. The result is 0.40 × 0.05 = 0.02, indicating a 2% chance of missing both shots.

Step-by-step explanation:

To find the probability of missing both free throw shots, you need to multiply the probability of missing the first shot by the probability of missing the second shot, given that the first was already missed. The student misses the first shot 40% of the time, which is a probability of 0.40. If she misses the first shot, she misses the second one 5% of the time, meaning there's a 0.05 probability of missing the second shot after missing the first one.

Now, calculate the probability of missing both:

Probability of missing the first shot (P(Miss 1st)) = 0.40

Probability of missing the second shot given the first is missed (P(Miss 2nd | Miss 1st)) = 0.05

The combined probability of missing both shots is:

P(Miss both) = P(Miss 1st) × P(Miss 2nd | Miss 1st) = 0.40 × 0.05 = 0.02

Therefore, the probability of missing both free throw shots is 0.02 or 2%.

Answer 2

45% probability that she will miss both free throw shots