A basketball player normally has a 70% chance of making a free throw. The player shoots until finally making a basket, where $x$ is the number of shots they take. Is this a binomial experiment?

• A. Yes
• B. No, there are not 2 outcomes
• C. No, there are not a fixed # of trials
• D. No, the trials are not independent
• E. No, the probability of success is not the same for each trial

Answer: (C)

Verified step by step guidance

1. Understand the definition of a binomial experiment: A binomial experiment consists of a fixed number of trials, each trial is independent, there are only two possible outcomes (success or failure), and the probability of success is the same for each trial.
2. Identify the characteristics of the given scenario: The player shoots until making a basket, which means the number of trials is not fixed. This violates one of the key conditions of a binomial experiment.
3. Consider the independence of trials: In a binomial experiment, each trial must be independent. In this scenario, the trials are independent because the outcome of one shot does not affect the outcome of another.
4. Evaluate the number of outcomes: There are two possible outcomes for each shot - either the player makes the basket (success) or misses (failure). This condition is satisfied.
5. Assess the probability of success: The probability of making a basket is 70% for each shot, which remains constant. This condition is satisfied. However, due to the lack of a fixed number of trials, this scenario is not a binomial experiment.