When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 25 or to bet $5 that the outcome is any one of the three possibilities 00, 0, or 1. The gambler knows that the expected value of the $5 bet for a single number is -0.26¢. For the $5 bet that the outcome is 00, 0, or 1, there is a probability of 3/38 of making a net profit of $20 and a 35/38 probability of losing $5.
Find the expected value for the $5 bet that the outcome is 00, 0, or 1.
Which bet is better: a $5 bet on the number 25 or a $5 bet that the outcome is any one of the numbers 00, 0, or 1? Why?