Suppose in a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the box containing it. Before each game, the old prize is removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice? Check each of the requirements of a binomial experiment.


Yes, the five trials are independent, repeated under the same conditions, have only two outcomes, and have the same probability of success.

No, the five trials are independent, repeated under the same conditions; have only two outcomes but they do not have the same probability of success.

Yes, the five trials are dependent, repeated under the same conditions, have only three outcomes, and have the same probability of success.

No, the five trials are dependent, repeated under the same conditions; have only two outcomes, but they do not have the same probability of success.

No, the five trials are independent, have only two outcomes, and have the same probability of success, but are not repeated under the same conditions.

No, the correct answer is:

No, the five trials are independent, repeated under the same conditions; have only two outcomes but they do not have the same probability of success.

To determine if it is appropriate to use the binomial probability distribution, we need to check the requirements of a binomial experiment. These requirements include:

1. Independent Trials: Each trial must be independent, meaning that the outcome of one trial does not affect the outcome of another trial.

2. Fixed Number of Trials: The number of trials must be fixed in advance.

3. Two Outcomes: Each trial must have only two possible outcomes – success or failure.

4. Constant Probability of Success: The probability of success must be the same for each trial.

In this carnival game scenario, we have five trials where a contestant plays the game five times. The number of trials is fixed in advance, and each trial has only two outcomes – either the contestant wins the prize or they do not. However, the probability of success is not the same for each trial. Before each game, the old prize is removed, and another prize is placed at random in one of the six boxes. This means that the probability of winning the prize is not constant across all five trials.

Therefore, it is not appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice.