Determine which of the following probability experiments qualify as binomial experiments. For those that are binomial experiments, identify the number of trials, probability of success, probability of failure, and possible values of the random variable X.

(a) An experiment in which a basketball player who historically makes 80% of his free throws is asked to shoot three free throws, and the number of free throws made is recorded.

(b) According to a recent Harris Poll, 28% of Americans state that chocolate is their favorite flavor of ice cream. Suppose a simple random sample of size 10 is obtained and the number of Americans who choose chocolate as their favorite ice cream flavor is recorded.

(c) A probability experiment in which three cards are drawn from a deck without replacement and the number of aces is recorded.

Approach Determine whether the four conditions for a binomial experiment are satisfied.

1. The experiment is performed a fixed number of times.

2. The trials are independent.

3. There are only two possible outcomes of the experiment.

4. The probability of success for each trial is constant.