Question

In a game, you have a 1/36 probability of winning $94 and a 35/36 probability of losing $8. What is your expected value?

Answer 1

\[\text{expected winnings}=\sum_{\text{all outcomes}}\text{(prob. of outcome)(win/loss of outcome)}\]
In this case, there are two outcomes, winning $94 and losing $8. Each has a respective probability of \(\dfrac{1}{36}\) and \(\dfrac{35}{36}\), which means
\[\text{expected winnings}=\frac{1}{36}(94)+\frac{35}{36}(-8)\approx-5.17\]
This means you should expect to lose $5.17 if you choose to play.