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1. The probability of selecting a student at Bovine University who is less than 20 years old is .46. The probability of selecting a student who is greater than 20 years old is .31. What is the probability of selecting a student who is 20 years old?

Prob(20) = 1 - Prob(not 20) = 1 - .77 = .23

2 A game of chance has four possible outcomes. The probability of outcome A is .30. The probability of outcome B is .20. The probability of outcome C is .40. What is the probability of outcome D?

The probability of A, B, or C is .3 + .2 + .4 = .9. The only other option is D, which must have 1 - .9 = .1 probability.

3. My kids used to play dungeons and dragons, and for that game they needed an amazing assortment of dice. The fewest faces a die can have is four (each side is a triangle, one side is down and three are up). Suppose a four-sided die is constructed so 35% of the time it will have side 1 on the bottom, 30% of the time side 2 will be on the bottom, and 25% of the time side 3 will be on the bottom. What is the probability that the fourth side will end up on the bottom?

Same logic as for 2. The answer is .1

4. A person is playing a game similar to "Who wants to Be A Millionaire" in which a person must answer a series of multiple-choice questions. He knows nothing, but is willing to guess. If he guesses right on the first try, he can go on to the second try. Each question has four possible answers, so the probability of getting a right answer in a round is .25. If the game lasts two rounds, there are three possible outcomes: None right, one right and one wrong, and two right. What are the probabilities for these three outcomes?

The only way to get none right is to miss the first question, and he has a .75 probability of doing that. The probability of getting both right means that he gets the first one right, which has a .25 probability, and then given that he had done that, getting the next one right, which also has a .25 probability. Multiplying them gives a probability of .0625. The probability of getting either both correct or none correct is .75 + .0625 = .8125. The probability of getting one right and one wrong, which is the only other option, is 1 - .8125 = .1875.

5. Suppose that the probability that a car salesman will sell two or more cars in a day is .22. What is the probability that he will sell less than two cars in a day?

1 - .22 = .78

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