Question

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? yes, a success is ace. yes, all four conditions in bins have been met. no, we do not know how many aces will occur in those first four cards. no, the cards are not being replaced, so the independence condition is not met.

Explanation:

For a binomial setting, the following conditions (BINS) must be met:

• Binary outcomes (success/failure). Here, success is "ace" and failure is "non - ace", so this condition is met.
• Independence: The trials must be independent. When cards are not replaced (as in this case, turning over 4 cards one - at - a - time without replacement), the probability of getting an ace on the second draw depends on what happened on the first draw. For example, if the first card is an ace, the probability of the second card being an ace is \(\frac{3}{51}\), and if the first card is not an ace, the probability of the second card being an ace is \(\frac{4}{51}\).
• Number of trials: There is a fixed number of trials (\(n = 4\) in this case).
• Same probability of success on each trial: Since the cards are not replaced, the probability of success (getting an ace) changes from trial to trial.

Answer:

No, the cards are not being replaced, so the independence condition is not met.