Chapter 15.11, Problem 8MP

(a) A weighted coin has probability $\frac{2}{3}$ of coming up heads and probability $\frac{1}{3}$ of coming up tails.

The coin is tossed twice. Let $x=$ number of heads. Set up the sample space for $x$ and the associated probabilities.

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

(c) If in (a) you know that there was at least one tail, what is the probability that both were tails?