Question

When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 34 or to bet 15 that the outcome is any one of the five possibilities 00 comma 0 comma 1 comma 2 comma or 3. The gambler knows that the expected value of the $15 bet for a single number is negative 0.79 cents. For the $15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3, there is a probability of 5/38 of making a net profit of $75 and a 33/38 probability of losing $15.

a. Find the expected value for the €‹$15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3.

Answer 1

The expected value for a $15 bet that the outcome is 00, 0, 1, 2, or 3 is $0.99.

Step-by-step explanation:

The expected value of a $15 bet that the outcome is any one of the five possibilities 00, 0, 1, 2, or 3 can be calculated as follows:

1. Probability of making a net profit of $75 = 5/38
2. Probability of losing $15 = 33/38

Multiply the probability of making a profit ($75) by its corresponding probability (5/38), and multiply the probability of losing ($15) by its corresponding probability (33/38).

Expected Value = (Probability of making a profit x Amount of profit) + (Probability of losing x Amount of loss)

Expected Value = (5/38 x $75) + (33/38 x -$15)

Expected Value = $0.99