20. A gambling book recommends the following "winning strategy" for the game of roulette. It recommends that a gambler bet $1 on red. If red appears

(which has probability $\frac{18}{38}$), then the gambler should take her $1 profit and quit. If the gambler loses this bet (which has probability $\frac{20}{38}$ of occurring), she should make additional $1 bets on red on each of the next two spins of the roulette wheel and then quit. Let X denote the gambler's winnings when she quits.

(a) Find P{X > 0).

(b) Are you convinced that the strategy is indeed a "winning" strategy?

Explain your answer!

(c) Find E[X].