Determine whether the following probability experiment repre

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. Four cards are selected from a standard 52-card deck without replacement. The number of fives selected is recorded. Does the probability experiment represent 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 the experiment is not performed a fixed number of times. No, because there are more than two mutually exclusive outcomes for each trial. Yes because the experiment satisfies all the criteria for a binomial experiment.

Solution

OPTION A: No, because the trials of the experiment are not independent and the probability of success differs from trial to trial. [ANSWER, A]

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For example, at the first draw, you can draw a 5 with 4/52 probability.

However, the second draw would depend on whether or not you have drawn a 5 on the first try, as there will be fewer fives if you did.

Hence, they are not independent, so it is not a binomial.