Question

When playing roulette at a​ casino, a gambler is trying to decide whether to bet ​$10 on the number 29 or to bet ​$10 that the outcome is any one of the three possibilities 00, 0, or 1. The gambler knows that the expected value of the ​$10 bet for a single number is −$1.06. For the ​$10 bet that the outcome is 00, 0, or 1​, there is a probability of 3/38 of making a net profit of ​$40 and a 35/38 probability of losing ​$10. a. Find the expected value for the ​$ 10 bet that the outcome is 00, 0, or 1.

a) $0.53
b) $0.79
c) $1.06
d) $1.33

Answer 1

The expected value of the $10 bet that the outcome is 00, 0, or 1 in roulette is an approximate loss of $6.05, indicating that in the long run a player would lose money on this bet. ooption B is correct.

Step-by-step explanation:

To find the expected value of the $10 bet that the outcome is 00, 0, or 1, we use the following formula:

Expected value = (Net profit x Probability of winning) + (Loss x Probability of losing).

Given that the net profit is $40 with a probability of 3/38, and the loss is $10 with a probability of 35/38, the calculation would be:

Expected value = ($40 x 3/38) + (-$10 x 35/38)

Expected value = ($120/38) - ($350/38)

Expected value = $120/38 - $350/38

Expected value = -$230/38

Expected value = - $6.0526 (approximately)

After rounding to the nearest cent, the expected value is about -$6.05, which means that in the long run, the player would expect to lose approximately $6.05 per game on this $10 bet.