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

please help

To determine whether it is appropriate to use the binomial probability distribution for this scenario, we need to check each of the requirements of a binomial experiment:

1. Independent Trials: The question states that the trials are independent, meaning the outcome of each trial does not depend on the outcome of previous trials.

2. Same Conditions: The question states that the trials are repeated under the same conditions, implying that the rules and probabilities do not change between trials.

3. Two Outcomes: The question states that there are two possible outcomes - winning the prize or not winning the prize.

4. Same Probability of Success: The question does not explicitly state whether the probabilities of winning in each game are equal.

Based on the information provided, we can conclude that the binomial probability distribution can be used if the probability of winning in each game is the same. However, if the probabilities of winning differ between games, then it would not be appropriate to use the binomial distribution.

To determine if it is appropriate to use the binomial probability distribution for this scenario, we need to check each of the requirements of a binomial experiment:

1. Independent trials: In this scenario, the trials are independent because the outcome of one trial does not affect the outcome of the others. Each time, the prize is placed at random in one of the six boxes. So, the first requirement is satisfied.

2. Repeated under the same conditions: The game is played five times, and each time the old prize is removed and a new prize is placed randomly in one of the six boxes. This condition is also satisfied.

3. Two outcomes: The contestant either wins the prize by selecting the correct box or does not win. This condition is satisfied.

4. Same probability of success: Since there is only one prize and it is randomly placed in one of the six boxes, the probability of winning is the same for each trial. This condition is also satisfied.

Based on the analysis above, we can conclude that it is appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice.

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