In Las Vegas, roulette is played on a wheel with 38 slots, of which 18 are black, 18 are red, and 2 are green (zero and double-zero). Your friend impulsively takes all $361 out of his pocket and bets it on black, which pays 1 for 1. This means that if the ball lands on one of the 18 black slots, he ends up with $722, and if it doesn't, he ends up with nothing.

Once the croupier releases the ball, your friend panics; it turns out that the $361 he bet was literally all the money he has. While he is risk-averse his utility function is u(x) = x, where x is his roulette payoff you are effectively risk neutral over such small stakes.

a. When the ball is still spinning, what is the expected profit for the casino?

b. When the ball is still spinning, what is the expected value of your friend's wealth?

c. When the ball is still spinning, what is your friend's certainty equivalent (i.e., how much money would he accept with certainty to walk away from his bet).

Say you propose the following transaction: while the ball is still spinning, you pay your friend $300 in exchange for the rights to the roulette winnings.

d. Is this bet worthwhile for you to offer? Why or why not?