in a game of roulette, there are 18 red numbers, 18 black numbers, and 2 green numbers. you may bet on red or black, but not green. if you win a $1 bet on the color, the house pays you $1. what is the expected value of each $1 you play at this game
expected value:
1(36/38) . So you lose money.
-$.05
To calculate the expected value, we can multiply the probability of each outcome by the corresponding payout and sum them up.
In a game of roulette, there are 18 red numbers, 18 black numbers, and 2 green numbers. Since you can only bet on red or black, there are a total of 36 possible outcomes.
The probability of winning by betting on red or black is 18/36 or 1/2, as there are 18 red numbers and 18 black numbers.
If you win a $1 bet, the house pays you $1. Therefore, the payout in this case is 1.
To calculate the expected value, multiply the probability of winning by the payout:
Expected Value = (Probability of Winning) x (Payout)
Expected Value = (1/2) x (1) = 1/2
Hence, the expected value of each $1 you play in this game is $0.50.
To calculate the expected value of each $1 played in this game, we need to multiply the amount you can win by the probability of winning and then subtract the amount you can lose multiplied by the probability of losing.
In this case, you can win $1 and the probability of winning is 18 out of 38 numbers (since there are a total of 38 numbers on the roulette wheel). Therefore, the probability of winning is 18/38.
You can also lose $1 if the ball lands on one of the 20 numbers that are not red or black (the two green numbers). Therefore, the probability of losing is 20 out of 38 numbers.
Now, let's calculate the expected value:
Expected value = (Amount won * Probability of winning) - (Amount lost * Probability of losing)
Expected value = ($1 * 18/38) - ($1 * 20/38)
Expected value = ($18/38) - ($20/38)
Expected value = -$2/38
Therefore, the expected value of each $1 you play at this game is -$2/38. This means that, on average, you are expected to lose approximately $0.053 per $1 played.