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Question 3 (20 points): A person tosses three dice at once. He wins if there are at least two six appearing. This person plays 5 times. a. Find the probability that the person wins at least 2 times. b. How does the answer in (a) change if after each tossing, the previous numbers cannot appear anymore. For example: if 1 appears in the first toss, there are only 5 outcomes in the second toss (two to six with equal chances), and so on. c (**) (extra 5 points). Imagine you want to cheat and can increase the chance of the number 6 to your desire. Compute the minimum chance of the number 6 to make sure the probability in (a) increases to 50%.

          Question 3 (20 points): A person tosses three dice at once. He wins if there are at least two six appearing. This person plays 5 times.
a. Find the probability that the person wins at least 2 times.
b. How does the answer in (a) change if after each tossing, the previous numbers cannot appear anymore. For example: if 1 appears in the first toss, there are only 5 outcomes in the second toss (two to six with equal chances), and so on.
c (**) (extra 5 points). Imagine you want to cheat and can increase the chance of the number 6 to your desire. Compute the minimum chance of the number 6 to make sure the probability in (a) increases to 50%.

Question 3 (20 points): A person tosses three dice at once. He wins if there are at least two six appearing. This person plays 5 times.
a. Find the probability that the person wins at least 2 times.
b. How does the answer in (a) change if after each tossing, the previous numbers cannot appear anymore. For example: if 1 appears in the first toss, there are only 5 outcomes in the second toss (two to six with equal chances), and so on.
c (**) (extra 5 points). Imagine you want to cheat and can increase the chance of the number 6 to your desire. Compute the minimum chance of the number 6 to make sure the probability in (a) increases to 50%.

Added by Dawn G.

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