In a standard roulette wheel, there are 18 red numbers out of a total of 38 numbers (18 red, 18 black, and 2 green).
The probability of the ball landing on a red number is therefore 18/38, or 9/19.
If the player bets $5, the player will win $5 if the ball lands on a red number.
The expected value (or expectation) is calculated by multiplying the probability of winning by the amount won, and subtracting the probability of losing multiplied by the amount lost.
Expectation = (probability of winning)(amount won) - (probability of losing)(amount lost)
Expectation = (9/19)(5) - (10/19)(5)
Expectation = (45/19) - (50/19)
Expectation = -5/19
Therefore, the player's expectation is -$5/19. This means that on average, the player can expect to lose approximately $0.26 per $1 bet on a red number.
One of the wagers in the game of roulette is to place a bet that the ball will land on a red number. If the ball lands on a red number, the player wins the amount of his bet. If a player bets $5, find the player's expectation.
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