When playing roulette at a casino, a gambler is trying to decide whether to bet $1010 on the number 1313 or to bet $1010 that the outcome is any one of the threethree possibilities 00 comma 0 comma or 100, 0, or 1. The gambler knows that the expected value of the $1010 bet for a single number is negative $ 1.06−$1.06. For the $1010 bet that the outcome is 00 comma 0 comma or 100, 0, or 1, there is a probability of StartFraction 3 Over 38 EndFraction
3
38 of making a net profit of $4040 and a StartFraction 35 Over 38 EndFraction
35
38 probability of losing $1010.
a. Find the expected value for the $1010 bet that the outcome is 00 comma 0 comma or 100, 0, or 1.
b. Which bet is better: a $1010 bet on the number 1313 or a $1010 bet that the outcome is any one of the numbers 00 comma 0 comma or 100, 0, or 1? Why?