Question

The probability that Rahul succeeds at any given free-throw is70. He was curious how many free-throws he can expect to succeed in a sample of 15 free-throws. He siμlated 30 samples of 15 free-throws where each free-throw had a 0.7 probability of being successful.

a) Provide the expected number of successful free-throws.
b) Insufficient information to answer.
c) Perform the necessary calculations.
d) The probability is undefined.

Answer 1

In a binomial problem with a 70% success rate for each free-throw, Rahul can expect to make approximately 10.5 out of 15 free throws.

Step-by-step explanation:

Expected Number of Successes in Binomial Problems

Rahul has a 70% probability of succeeding at any given free-throw. If he takes a sample of 15 free-throws, we can calculate the expected number of successful free-throws using the formula for the expected value in a binomial distribution: E(X) = n * p, where 'n' is the number of trials, and 'p' is the probability of success on each trial.

In Rahul's case:

• Number of trials (n) = 15
• Probability of success (p) = 0.7

Therefore, the expected number of successful free-throws (E(X)) would be:

E(X) = 15 * 0.7 = 10.5

Rahul can expect to make approximately 10.5 free throws in a sample of 15 attempts. This is a binomial problem because there are two outcomes (success or failure), and the probability of success remains constant at 0.7 for each free-throw attempt.