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6.[total 7] I roll a fair die 500 times. What is the approximate probability that I obtain(a) [2] exactly 100 sixes?(b) [2] at least 95 sixes?(c) [3] I carry out this experiment 200 times. What is the approximate probability thatI roll exactly 100 sixes at least twice?
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7.[total 10] I have three dice. One is six-sided, one is eight-sided, and one is twelve-sided.Then-sided die has numbers 1 throughnon its sides, and each side is equally likely to comeup. I roll the three dice.(a) [2] What is the probability that I roll the same number on all three dice?(b) [2] What is the probability that theproductof the three numbers I roll is even?(Hint: the product of two odd numbers is odd; the product of an even number with anyother number is even.)(c) [3] What is the probability that thesmallestnumber I roll is a 3?(d) [3] I pick one of the dice at random, with all three equally likely to be picked. I rollit and it comes up 4. What’s the probability the die I rolled was the six-sided die?
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