Question

basketball player Sheryl Swoopes scores on 85% of her foul shots. If Swoopes has eight foul shots during a game, what is the probability that she will score on exactly seven of them?

Answer 1

probability p = 0.85

number of total foul shots (n) = 8

we have to find P(X = 7)

binomial formula can be used here,

Answer 2

To find the probability that Sheryl Swoopes will score on exactly seven out of eight foul shots, we can use the binomial probability formula. The formula for calculating the probability of getting exactly k successes in n trials, where the probability of success in each trial is p, is:

P(X = k) = (n C k) * p^k * (1 - p)^(n - k)

Where: P(X = k) is the probability of getting exactly k successes (n C k) represents the number of combinations of n items taken k at a time p is the probability of success in a single trial (1 - p) is the probability of failure in a single trial n is the total number of trials

In this case, Sheryl Swoopes scores on 85% of her foul shots, which means the probability of success in a single trial is p = 0.85. The total number of foul shots is n = 8, and we want to calculate the probability of scoring on exactly seven of them, so k = 7.

Using the formula, we can calculate the probability:

P(X = 7) = (8 C 7) * (0.85)^7 * (1 - 0.85)^(8 - 7)

To simplify the calculation: (8 C 7) = 8 (0.85)^7 = 0.2874 (1 - 0.85)^(8 - 7) = 0.15

P(X = 7) = 8 * 0.2874 * 0.15

P(X = 7) ≈ 0.3441

Therefore, the probability that Sheryl Swoopes will score on exactly seven out of eight foul shots is approximately 0.3441, or 34.41%.