Find the probability

Question

A basketball player has a 80% chance of making each free throw. What is the probability that the player makes exactly eight out of ten free throws?

Answer 1

This Problem has to do with a Binomial Distribution.

Since the basketball player has a 80% chance of making each free throw, and you are given that there are 10 free throws, then it follows a Binomial Distribution with parameters p, and n.

p stands for the probability of success (P=0.80)

n stands for the total of outcomes (free throws) (n=10).

By following the formula for binomial distribution: P(X=x) = (nCx)(p^x)(1-p)^(n-x), we can easily compute the probability of 8 free throws.(Note that the C between the n and x, stands for combination formula).

P(X=8) = (10C8)(0.80)⁸(1-0.80)^10-8=(45)(0.80)⁸(0.20)²= 0.30198 = 30.198%