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.
my answer was the second choice am i CORRECT
What outcomes do you have? (win/don't win)
In what way (if any) do the following events depend on the previous ones?
What is the probability of success on each trial?
Answering these questions should lead you to the correct answer.
No, your answer is not correct.
An appropriate use of the binomial probability distribution requires that the experiment satisfies four requirements:
1. The trials are independent: In this case, each game is considered a separate and independent trial since the old prize is removed and a new prize is placed randomly in one of the boxes before each game. Thus, this requirement is met.
2. Repeated under the same conditions: The game is played five times, and each time the same rules and conditions apply. So, this requirement is also met.
3. Have only two outcomes: The contestant either wins the prize or does not win it. This is indeed a two-outcome experiment, so this requirement is met.
4. Same probability of success: The success in this case is defined as the contestant winning the prize. Since each box has an equal chance of containing the prize, the probability of success is the same for each trial. Therefore, this requirement is also fulfilled.
Based on these requirements, the appropriate answer to the question is the first choice: "Yes, the five trials are independent, repeated under the same conditions, have only two outcomes, and have the same probability of success."