Chapter 15.11, Problem 2MP

(a) Suppose that Martian dice are regular tetrahedra with vertices labeled 1 to 4. Two such dice are tossed and the sum of the numbers showing is even. Let $x$ be this sum. Set up the sample space for $x$ and the associated probabilities.

(b) Find $E(x)$ and ${\sigma }_x$.

(c) Find the probability of exactly fifteen 2’s in 48 tosses of a Martian die using the binomial distribution.

(d) Approximate (c) using the normal distribution.

(e) Approximate (c) using the Poisson distribution.