Expected Value in Roulette 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 6 , we know that the expected value of the $\$ 5$ bet for a single number is $-26 \phi$. 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 any one of the numbers $0,00,1,2$, or $3 ?$ Why?