8
QuizMultiple Choice

Binomial Random Variables

Question 8 • College Prep Math B - IC26

Ian shuffles a standard deck of 52 playing cards and turns over the first four cards, one at a time. He records the number of aces he observes.Have the conditions for a binomial setting been met for this scenario?

Answer
A
Yes, a success is “ace.”
B
Yes, all four conditions in BINS have been met.
C
No, we do not know how many aces will occur in those first four cards.
D
No, the cards are not being replaced, so the independence condition is not met.

Explanation

There are a fixed number of trials (four), and each card can be classified as an ace or not an ace. However, the cards are drawn without replacement, so the probability of an ace changes after each card and the draws are not independent. Therefore, the binomial conditions are not met; choice D is correct.

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