Answer:
You are expected to lose $0.05 (or win -$0.05)
Step-by-step explanation:
Since the roulette wheel has the numbers 1 through 36, 0, and 00, there are 38 possible outcomes.
In this bet, you are allowed to pick 3 out of the 38 numbers. Thus, your chances of winning (P(W)) and losing (P(L)) are:
![P(W)=\frac{3}{38}\\P(L) = 1 - P(W)\\P(L) = \frac{35}{38}\\](https://tex.z-dn.net/?f=P%28W%29%3D%5Cfrac%7B3%7D%7B38%7D%5C%5CP%28L%29%20%3D%201%20-%20P%28W%29%5C%5CP%28L%29%20%3D%20%5Cfrac%7B35%7D%7B38%7D%5C%5C)
The expected value of the bet is given by the sum of the product of each outcome pay by its probability. Winning the bet means winning $11 while losing the bet means losing $1. The expected value is:
![EV = (11*\frac{3}{38}) -(1*\frac{35}{38})\\EV = -\$0.0525](https://tex.z-dn.net/?f=EV%20%3D%20%2811%2A%5Cfrac%7B3%7D%7B38%7D%29%20-%281%2A%5Cfrac%7B35%7D%7B38%7D%29%5C%5CEV%20%3D%20-%5C%240.0525)
Therefore, with a $1 bet, you are expected to lose roughly $0.05