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Probability of Rolling die problem

A fair die is rolled (independently) 12 times.

(a) Let X denote the total number of 1’s in 12 rolls. Find the expected value and variance of X.

(b) Determine the probability of obtaining exactly four 1’s.

(c) Determine the probability of obtaining at least one 1.

(d) Approximate the probability in part (b) using Poisson approximation to binomial distribution. What is the percent relative error of approximation (round the answer off to two decimal places)?

(e) Approximate the probability in part (c) using Poisson approximation to binomial distribution. What is the percent relative error of approximation (round the answer off to two decimal places)?

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