When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 28 or to bet $5 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 $5 bet for a single number is -0.26. For the $5 bet that the outcome is 00, 0, 1, 2, or 3, there is a probability of 5/38 of making a net profit of $30 and a probability of 33/38 of losing $5.
a. Find the expected value for the $5 bet that the outcome is 00, 0, 1, 2, or 3.
b. Which bet is better: a $5 bet on the number 28 or a $5 bet that the outcome is any one of the numbers 00, 0, 1, 2, or 3? Why?
a. The expected value is $0.13.
b. Since the expected value of the bet on the number 28 is less than the expected value for the bet that the outcome is 00, 0, 1, 2, or 3, the bet on the single number 00, 0, 1, 2, or 3 is better.