One of the wagers in the game of roulette is to place a bet that the ball will land on a black number. (Eighteen of the numbers are black, 18 are red, and two are green.) If the ball lands on a black number, the player wins the amount of his bet. If a player bets $7, find the player's expectation.

Step-by-step explanation:

Given that one of the wagers in the game of roulette is to place a bet that the ball will land on a black number.

Probability will be 18/38 for black and red and 2/38 for green

We have

Colour Black Red Green Total

Number 18 18 2 38

Bet amt. 7 7 7

Win amt. 7 0 0

Net win 0 - 7 - 7

Prob 18/38 18/38 2/38

Netwin*p 0 - 126/38 - 14/38

Expected value of win = - 140/38 = - 3.68