A gambling book recommends the following “winning strategy” for the game of roulette: Bet $1 on red. If red appears (which has probability 18/38), then take the $1 profit and quit. If red does not appear and you lose this bet (which has probability 20/38 of occurring), make additional $1 bets on red on each of the next two spins of the roulette wheel and then quit. Let X denote your winnings when you quit.
(a) Find P{X > 0}.
(b) Are you convinced that the strategy is indeed a “winning” strategy? Explain your answer!
(c) Find E[X].