Question

John's free throw shooting percentage is 87%. If John shoots 12 free throws in the course of a game, what is the probability he makes exactly 10?

Answer 1

Answer:

0.2771

Step-by-step explanation:

This is a binomial probability question.  "Makes" is what some writers call a "success."  In the binomial probability distribution, the probability of  r  successes in  n  trials is

$\binom{n}{r}p^r(1-p)^{n-r}$

p is the probability of "success."  $\binom{n}{r}=\frac{n!}{r!(n-r)!}$

In this problem, n = 12,  r = 10, p = 0.87 (the 87%).

The probability of exactly 10 made shots out of 12 attempted is

$\binom{12}{10}(0.87)^10(1-0.87)^2 =66(0.87^10)(0.13)^2 \approx 0.2771$