Question

In American roulette, the wheel contains the numbers 1 through 36, alternating between black and red. There are two green spaces numbered 0 and 00. A player places a bet of $9.00 on red to play the game. If the ball lands on red, the player gets $9.00 for winning and receives the money back. If the ball does not land on red, then the player simply loses the $9.00 placed on the bet. If the player places the same bet on red 24 times, what is the player's expected winnings? Round your answer to the nearest cent.

Answer 1

The player's expected winnings per round in American roulette is -$0.474.

Step-by-step explanation:

The player's expected winnings can be calculated by finding the probability of winning and losing each round and multiplying it by the amount won or lost in each round. In this case, the player's bet is $9.00 on red. The probability of winning in American roulette is 18/38 (since there are 18 red numbers out of 38 total numbers). So the player's expected winnings per round can be calculated as:

Expected winnings = (Probability of winning * Amount won) + (Probability of losing * Amount lost)

= (18/38 * $9.00) + (20/38 * (-$9.00))

= -$0.474

Therefore, the player's expected winnings per round is -$0.474, which means the player can expect to lose approximately $0.474 per round.