When playing roulette at a casino, a gambler is trying to decide whether to bet $20 on the number 29 or to bet $20 that the outcome is any one of the three possibilities 00, 0, or 1. The gambler knows that the expected value of the $20 bet for a single number is -$2.10. For the $20 bet that the outcome is 00, 0, or 1, there is a probability of 3/38 of making a net profit of $60 and a 35/38 probability of losing $20.
a. Find the expected value for the $20 bet that the outcome is 00, 0, or 1.
b. Which bet is better: a $20 bet on the number 29 or a $20 bet that the outcome is any one of the numbers 00, 0, or 1? Why?