When playing roulette at the Bellagio casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 13 or to bet $5 that the outcome is any one of these five possibilities: 0 or 00 or 1 or 2 or 3. From Example 8, we know that the expected value of the $5 bet for a single number is -26⊄. For the $5 bet that the outcome is 0 or 00 or 1 or 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 or 00 or 1 or 2 or 3.

b. Which bet is better: A $5 bet on the number 13 or a $5 bet that the outcome is 0 or 00 or 1 or 2 or 3? Why?