A die is loaded so that even numbers occur three times as often as odd numbers.

(a) If the die is thrown N = 12 times, what is the probability that odd numbers occur three times? If it is thrown N = 120 times, what is the probability that odd numbers occur thirty times? Use the binomial distribution.

(b) Compute the same quantities as in part

(a) but use the Gaussian distribution. [Note: For parts

(a) and

(b) compute your answers to four places.]

(c) Compare answers for

(a) and (b). Plot the binomial and Gaussian distributions for the case N = 12.