# Question

Consider the following games with two dice.

a. A gambler is going to roll a die four times. If he rolls at least one 6, you must pay him $5. If he fails to roll a 6 in four tries, he will pay you $5. Find the probability that you must pay the gambler. Assume that there is no cheating.

b. The same gambler offers to let you roll a pair of dice 24 times. If you roll at least one double 6, he will pay you $10. If you fail to roll a double 6 in 24 tries, you will pay him $10. The gambler says that you have a better chance of winning because your probability of success on each of the 24 rolls is 1/36 and you have 24 chances. Thus, he says, your probability of winning $10 is 24(1/36) = 2/3. Do you agree with this analysis? If so, indicate why. If not, point out the fallacy in his argument, and then find the correct probability that you will win.

a. A gambler is going to roll a die four times. If he rolls at least one 6, you must pay him $5. If he fails to roll a 6 in four tries, he will pay you $5. Find the probability that you must pay the gambler. Assume that there is no cheating.

b. The same gambler offers to let you roll a pair of dice 24 times. If you roll at least one double 6, he will pay you $10. If you fail to roll a double 6 in 24 tries, you will pay him $10. The gambler says that you have a better chance of winning because your probability of success on each of the 24 rolls is 1/36 and you have 24 chances. Thus, he says, your probability of winning $10 is 24(1/36) = 2/3. Do you agree with this analysis? If so, indicate why. If not, point out the fallacy in his argument, and then find the correct probability that you will win.

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