Wen, who has current wealth of $10,000, decides to take advantage of a free trip to Las Vegas to play roulette. His utility function over the wealth he ends up with after the trip Y (which equals his current wealth adjusted by any amount he ends up winning or losing) is U(Y) = (Y. He can take one of two gambles at the roulette table:

Gamble 1. Wager $1,000 on red. If red comes up, which happens with probability 18/38, he wins

$1,000; otherwise he loses his $1,000 wager.

Gamble 2. Wager $500 on the single number 00. If 00 comes up, which happens with probability 1/38, he wins 35 times his wager ($17,500); otherwise he loses his $500 wager.

a. Are these fair gambles?

b. If Wen is forced to take one of the two gambles, which would he prefer?

c. If Wen isn't forced to play roulette, would he take a gamble?