Suppose insetad that you are told that lincoln is

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presidents? Suppose, insetad, that you are told that Lincoln is showing. What now is the probability of seeing three presidents? Why do the answers differ? (B+S 7.2.15) 3. Suppose someone has randomly generated two natural numbers and used them to make a fraction. Reduce the fraction to its lowest terms. Is there a 0.5 probability that both the numerator and the denominator are odd numbers? Why or why not? (B+S 7.2.29. Note that part of this question is to come up with a reasonable interpretation of the idea of a randomly generated natural number.) 4. Dungeons and Dragons players use dice in the shape of each of the regular solids. The faces are always numbered 1 through the number of total faces there are. You shake all five dice. what is the probability of your throwing a total of 6? (B+S 7.2.31) 5. Suppose you flip a fair coin 10 times on two different ocassions. One time you see 10 heads, the other time you see HHTHHHTTHT . Is either one of these outcomes more likely than the other? Which one is random? Explain. (B+S 7.3.31) 6. Suppose you deal three cards from a regular deck of 52 cards. What is the probability that they will all be jacks? (B+S 7.4.11) 7. (a) You roll a fair die four times. What is the probability that you see at least one 6? (b) You roll two fair dice twenty-four times. What is the probability that at least once, you see two 6s? (c) You bet someone, at even money, that upon rolling a fair die four times you will see at least one 6. You repeat this bet many times. Do you expect to win or lose money? (d) You bet someone, at even money, that upon rolling two fair dice twenty-four times you will, at least once, see two 6s. You repeat this bet many times. Do you expect to win or lose money? (Both bets mentioned here were bets that the Chevalier de Mere was interested in.) 1
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