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Suppose that a pair of fair dice are rolled 120 times. Let be the number of rolls on which the sum of the two numbers

Suppose that a pair of fair dice are rolled 120 times. Let be the number of rolls on which the sum of the two numbers is 12. Show your working details. You may use R to verify your answer.

(a)Find the probability when = 3 approximately using Poisson approximation.

(b)Compute the actual probability from binomial distribution. Comment on the accuracy of Poisson approximation.

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