A roulette wheel in Las Vegas has 18 red slots and 18 black slots numbered alternately with the numbers 1 through 36. Two green slots are numbered 0 and 00. The winning number is determined by the slot into which a single marble rolls. Players are not allowed to bet on green. The house wins all bets if 0 or 00 comes up. A $1 bet on a single roll of a roulette wheel wins $36 if the marble lands in the slot for the number selected. If that number doesn’t come the person placing the bet loses the $1. What is the expected value of such a bet?
expected value= reward*probability
= 36* 1/38 (ie, he has one chance in 38 to win, with a reward of 36)
To calculate the expected value of a bet, we need to consider the probability of winning and losing, as well as the amount won or lost.
In this case, the probability of winning is 1/38, as there are 38 slots on the roulette wheel. This is because there are 18 red slots, 18 black slots, and 2 green slots which are not eligible for betting.
If the selected number comes up, the person wins $36. If it doesn't come up, the person loses $1.
To calculate the expected value, we multiply the probability of winning by the amount won, and the probability of losing by the amount lost. Then we subtract the product of the losing probability and the amount lost from the product of the winning probability and the amount won.
Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
Expected value = (1/38 * $36) - (37/38 * $1)
Calculating this expression gives us the expected value:
Expected value = ($36/38) - ($37/38)
Expected value = -$1/38
Therefore, the expected value of the $1 bet on a single roll of a roulette wheel is approximately -$0.0263.
This means that, on average, a person will lose approximately $0.0263 for every $1 bet.