If a player placed a 8 bet on red and a 5 bet on black in a

If a player placed a $8 bet on red and a $5 bet on black in a single play in American roulette, what would be the expected value of his winnings? Round your answer to the nearest cent.

Solution

In the casino game of American roulette, the wheel is divided into 38 compartments numbered 1 through 36, 0, and 00.
One-half of the numbers 1 through 36 are red, the other half black, and 0 and 00 are green.

If a player placed a $8 bet on red and a $5 bet on black in a single play in American roulette,
Answers:   
Odds of bubble landing on red: 18/38
Odds of ball landing on black: 18/38
Odds of ball landing on green: 2/38

If ball lands on red, the network gain is zero (win $8 for red bet, lose $5 for black bet). Same thing if ball lands on black (win $5 for black bet, lose $8 for black bet). If globe lands on green, player loses $13 (both $8 red, %5 black bets are lost).

Expected value = 3 * 18/38 - 3 * 18/38 - 13 * 2/38 = -$0.6842