When you give the Venetian casino in Las Vegas $5 for a bet on the number 7 in roulette, you have a 37/38 probability of losing $5 and you have a 1/38 probability of making a net gain of $175. (The prize is $180, but your $5 bet is not returned, so the net gain is $175.) If you bet $5 that the outcome is an odd number, the probability of losing $5 is 20/38 and the probability of making a net gain of $5 is 18/38. (If you bet $5 on an odd number and win, you are given $10 that includes your bet, so the net gain is $5.)
a. If you bet $5 on the number 7, what is your expected value?
b. If you bet $5 that the outcome is an odd number, what is your expected value?
c. Which of these options is best: bet on 7, bet on odd, or don't bet? Why?