Determine whether the following probability experiment repre

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 fours 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 there are more than two mutually exclusive outcomes for each trial. No, because the experiment is not performed a fixed number of times. 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.