When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 13 or to bet $15 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 $15 bet for a single number is -$1.58. For the $15 bet that the outcome is 00, 0, 1, 2, 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, 0, 1, 2, or 3.
b. Which bet is better: a $15 bet on the number 13 or a $15 bet that the outcome is any one of the numbers 00, 0, 1, 2, or 3? Why