Determine whether the following probability experiment represents a binomial exp

Question

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. Five cards are selected from a standard 52-card deck without replacement. The number of aces selected is recorded. Does the probability experiment represent a binomial experiment? A. O B. O C. 0 D. No, because the experiment is not performed a fixed number of times. Yes, because the experiment satisfies all the criteria for a binomial experiment. No, because the trials of the experiment are not independent and the probability of success differs from trial to trial. No, because there are more than two mutually exclusive outcomes for each trial.

Explanation / Answer

The experiment can be attempted to be modelled as a binomial experiment.

Each card selected can be an ace or not and thus there are two outcomes.

However, since the selections happen to be dependent on each other, the experiment cannot be binomial.

The answer is:

C. No, because the trials of the experiment are not independent and the probability of success differes from trial to trial.

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