Question

which of the following are criteria for a binomial probability experiment?select all that applya. there are three mutually exclusive outcomes, arriving on - time, arriving early, and arriving lateb. the probability of success is the same for each trial of the experimentc. the trials are independentd. there are two mutually exclusive outcomes, success or failuree. the probability of success is different for each trial of the experimentf. the experiment is performed a fixed number of timesg. the experiment is performed until a desired number of successes is reachedh. each trial depends on the previous trial

Explanation:

• Option B: In a binomial probability experiment, the probability of success (\(p\)) remains constant for each trial. For example, if we are flipping a fair coin (where getting heads is a success), the probability of getting heads (\(p = 0.5\)) is the same for every flip.
• Option C: The trials in a binomial experiment are independent. If we are conducting an experiment of drawing cards with replacement (so that the outcome of one draw does not affect the next draw), the independence condition is met.
• Option D: A binomial experiment has two mutually - exclusive outcomes. For instance, in a quality - control test where an item is either defective (success, depending on the definition) or non - defective (failure).
• Option F: The binomial experiment is performed a fixed number of times (\(n\)). For example, if we are testing \(n = 10\) light bulbs for their functionality, \(n\) is pre - determined.

• Option A: A binomial experiment has only two mutually - exclusive outcomes, not three. So, this option is incorrect.
• Option E: In a binomial experiment, the probability of success is the same for each trial. If the probability of success changes from trial to trial, it is not a binomial experiment. So, this option is incorrect.
• Option G: A binomial experiment has a fixed number of trials. An experiment performed until a desired number of successes is reached is a negative - binomial or geometric experiment (in the case of \(r = 1\)). So, this option is incorrect.
• Option H: In a binomial experiment, trials are independent. If each trial depends on the previous trial, it violates the independence condition of a binomial experiment. So, this option is incorrect.

Answer:

B. The probability of success is the same for each trial of the experiment, C. The trials are independent, D. There are two mutually exclusive outcomes, success or failure, F. The experiment is performed a fixed number of times.