When playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 35 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 -$1.06. For the $10 bet that the outcome is 00, 0, 1, 2, or 3, there is a probability of 5/38 of making a net profit of $60 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 35 or a $10 bet that the outcome is any one of the numbers 00, 0, 1, 2, or 3? Why?