Question

QUESTION 1 OF 10

You are playing a game in which a single die is rolled. If a 2 or 5 comes up you win $36. Otherwise, you lose $36. What is your expected value for the game?

Answer 1

Let the dollar profit be X. For a win, the profit is $36. For a loss, the profit is -$36.
The probability of 2 or 5 is given by
\[P(2\ or\ 5)=\frac{1}{6}+\frac{1}{6}=\frac{1}{3}\]
The probability of 1, 3, 4 or 6 is given by
\[P(1, 3, 4\ or\ 6)=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{2}{3}\]

\[E(X)=(-36\times\frac{2}{3})+(36\times\frac{1}{3})=\ ?\ dollars\]