A basketball player has made 70% of his foul shots during the season.If he shoots 4 foul shots in tonight's game,what is the probability that he makes all of the shots?
A)0.0081
B)0.12
C)0.28
D)0.2401
E)0.7

Question

Quizplus · Accepted Answer

We can use the binomial probability formula to solve this problem:
P(X=k) = (n choose k) p^k (1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient (i.e., the number of ways to choose k items out of n).
In this case, n = 4, k = 4, p = 0.7, and (n choose k) = 1 (there is only one way to make all four shots). Thus,
P(X=4) = (4 choose 4) 0.7^4 (1-0.7)^(4-4) = 0.2401
Therefore, the probability that the basketball player makes all four shots is 0.2401, which is option D.

A Basketball Player Has Made 70% of His Foul Shots