Question

When playing roulette at a​ casino, a gambler is trying to decide whether to bet ​$10 on the number 33 or to bet ​$10 that the outcome is any one of the five possibilities 00, 0, 1, 2, or 3. The gambler knows that the expected value of the ​$10 bet for a single number is −53¢. For the ​$10 bet that the outcome is 00, 0, 1, 2, or 3​, there is a probability of 5 5/38 of making a net profit of ​$50 and a 33/38 probability of losing ​$10. a. Find the expected value for the ​$10 bet that the outcome is 00, 0, 1, 2, or 3 b. Which bet is​ better: a ​$10 bet on the number 33 or a ​$10 bet that the outcome is any one of the numbers 00, 0, 1, 2, or 3​? ​Why?

Answer 1

The expected value for the $10 bet that the outcome is 00, 0, 1, 2, or 3 is -$0.53, the same as the expected value for the $10 bet on the number 33.

Step-by-step explanation:

The expected value for the $10 bet that the outcome is 00, 0, 1, 2, or 3 can be calculated by multiplying the probability of making a net profit of $50 by the amount of profit, and adding it to the probability of losing $10 multiplied by the amount lost. In this case, the expected value is:

(5/38) * $50 + (33/38) * (-$10) = -$0.53

The expected value for the $10 bet on the number 33 is -$0.53. Comparing the two expected values, we can see that they are the same. Therefore, neither bet is better than the other, as they both result in an expected loss of -$0.53.