Suppose that your instructor rolls a pair of dice five times.

1. (a)What is the probability that the sum of the dice would be either 7 or 11 all five times, assuming that the dice were fair? [Hint: Let the random variable X represent the number of rolls in which the sum is 7 or 11, and use the binomial distribution to calculate this probability. You will first need to determine, the probability that the sum would be 7 or 11 on any one roll by listing the sample space of 36 equally likely outcomes. Then use that probability for the binomial parameter.] Show the details of your calculations, or technology output, to support your answer.

(b)Would this result (five consecutive rolls of 7 or 11) constitute reasonably strong evidence that the dice were not fair? Explain your reasoning, based on your answer to (a).

(c)Determine the probability of obtaining a sum of 7 or 11 innconsecutive rolls of a pair of fair dice as a function ofn, wherenis a positive integer.

(d)Graph this probability as a function ofn, and comment on the behavior of the function.

(e)Determine the smallest value ofnfor which this probability dips below 0.05. Then find the smallest such values ofnfor which the probability dips below 0.01, 0.001, and 0.00001.