When playing roulette at the Venetian casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 27 or to bet $5 that the outcome is any one of these five possibilities: 0, 00, 1, 2, 3. From Example 8, we know that the expected value of the $5 bet for a single number is -26c. For the $5 bet that the outcome is 0, 00, 1, 2, or 3, there is a probability of 5/38 of making a net profit of $30 and a 33/38 probability of losing $5.
a. Find the expected value for the $5 bet that the outcome is 0, 00, 1, 2, or 3.
b. Which bet is better: a $5 bet on the number 27 or a $5 bet that the outcome is 0, 00, 1, 2, or 3? Why?