5 name 6 total 7 i roll a fair die 500 times what is

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Name:
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 that
I roll exactly 100 sixes at least twice?
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Name:
7. [total 10] I have three dice. One is six-sided, one is eight-sided, and one is twelve-sided.
The n -sided die has numbers 1 through n on its sides, and each side is equally likely to come
up. 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 the product of the three numbers I roll is even?
(Hint: the product of two odd numbers is odd; the product of an even number with any
other number is even.)
(c) [3] What is the probability that the smallest number I roll is a 3?
(d) [3] I pick one of the dice at random, with all three equally likely to be picked. I roll
it and it comes up 4. What’s the probability the die I rolled was the six-sided die?
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