Final answer:
To find the probability of Jamal making exactly 8 out of 10 free-throws, we use the binomial probability formula, leading to a probability of around 23.35%.
Step-by-step explanation:
The question you have asked about Jamal's free-throw probability is a classic example of a binomial probability problem. In this instance, Jamal has a 70% chance of making each free-throw and he makes 10 shots.
To find the probability of him making exactly 8 out of 10 shots, we would use the binomial probability formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the combination of n things taken k at a time
- p is the probability of success on a single trial, which is 0.7 in this case
- (1-p) is the probability of failure on a single trial
- n is the number of trials
- k is the number of successes (in this case, 8)
When we calculate this out:
P(X=8) = C(10, 8) * 0.7^8 * 0.3^2
C(10, 8) is the number of combinations of choosing 8 successes from 10 trials, which is 45. Therefore:
P(X=8) = 45 * 0.7^8 * 0.3^2 = 0.2334744405, or about 23.35%.