4. A pair of fair dice are thrown 10 times. This question will be about a binomial distribution. Some event will be a "success" with probability p. Then calculate the probability that e.g. k = 3 or k< 2 or k > 0. 1 (a) What is the probability that the sum of the two dice is greater than 8 in exactly 4 of the 10 throws? (b) What is the probability that the sum of the two dice is greater than 8 for at least 2 of the 10 throws? (c) What is the expected number of times that the sum of the two dice is greater than 8?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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4. A pair of fair dice are thrown 10 times.
This question will be about a binomial distribution. Some event will
be a "success" with probability p. Then calculate the probability that
e.g. k = 3 or k< 2 or k > 0.
1
(a) What is the probability that the sum of the two dice is greater
than 8 in exactly 4 of the 10 throws?
(b) What is the probability that the sum of the two dice is greater
than 8 for at least 2 of the 10 throws?
(c) What is the expected number of times that the sum of the two
dice is greater than 8?
Transcribed Image Text:4. A pair of fair dice are thrown 10 times. This question will be about a binomial distribution. Some event will be a "success" with probability p. Then calculate the probability that e.g. k = 3 or k< 2 or k > 0. 1 (a) What is the probability that the sum of the two dice is greater than 8 in exactly 4 of the 10 throws? (b) What is the probability that the sum of the two dice is greater than 8 for at least 2 of the 10 throws? (c) What is the expected number of times that the sum of the two dice is greater than 8?
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