# Statistics

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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.

• Statistics -

You are playing a game with 3 prizes hidden behind 5 doors. One prize is worth \$100, another is worth \$20 and another \$10. You have to pay \$20 if you choose a door with no prize.What is your expected winning?