Question 12, 6.2.11
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Determine if the following probability experiment represents a binomial experiment. If not, explain why. If the probability experiment is a binomial experiment, state the number of trials, $\mathrm{n}$.

Four cards are selected from a standard 52-card deck without replacement. The number of nines selected is recordec

Select the correct choice below and, if necessary, fill in the answer box to complete your answer.
A. Yes, because the experiment satisfies all the criteria for a binomial experiment, $n=$
B. No, because the trials of the experiment are not independent since the probability of success differs from trial to trial.
C. No, because there are more than two mutually exclusive outcomes for each trial.
D. No, because the experiment is not performed a fixed number of times.

Step 1 ：The question is asking whether the given probability experiment is a binomial experiment or not. A binomial experiment is a statistical experiment that has the following properties: 1. The experiment consists of n repeated trials. 2. Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure. 3. The probability of success, denoted by P, is the same on every trial. 4. The trials are independent; the outcome on one trial does not affect the outcome on other trials.

Step 2 ：In this case, we are selecting four cards from a standard 52-card deck without replacement and recording the number of nines selected.

Step 3 ：This does not satisfy the conditions for a binomial experiment because the trials are not independent. The probability of drawing a nine changes with each draw, as cards are not replaced.

Step 4 ：Therefore, the answer is \(\boxed{\text{B. No, because the trials of the experiment are not independent since the probability of success differs from trial to trial.}}\)