Determine which of the following probability experiments...

Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why. A basketball player who makes $80 \%$ of her free throws is asked to shoot free throws until she misses. The number of free-throw attempts is recorded.

Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.
A basketball player who makes $80 \%$ of her free throws is asked to shoot free throws until she misses. The number of free-throw attempts is recorded.

Key Concepts

Constant Probability of Success

For an experiment to be considered binomial, the probability of success on each individual trial must be the same. This uniformity allows the application of the binomial probability formula to compute the distribution of outcomes.

Independent Trials

Independent trials mean that the result of one trial does not affect the outcomes of other trials. This independence ensures that the probability of success in each trial remains unchanged regardless of the results of previous trials.

Stopping Rule

The stopping rule in an experiment refers to the criteria used to determine when to end the sequence of trials. In a binomial experiment, the stopping rule is based on completing a fixed number of trials, not on achieving a particular outcome like the first failure or success, as that would result in a variable number of trials.

Binomial Experiment

A binomial experiment is a statistical experiment that satisfies a specific set of conditions: there is a fixed number of trials, each trial is independent, each trial results in one of two outcomes (commonly referred to as success or failure), and the probability of success remains constant from trial to trial.

Fixed Number of Trials

One of the defining features of a binomial experiment is that the number of trials is predetermined and does not change based on the outcomes observed during the experiment. The experiment must be carried out for a set, fixed number of trials.

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