A gambling book recommends the following “winning strategy” for the game of roulette: Bet...

A gambling book recommends the following “winning strategy” for the game of roulette: Bet $1 on red. If red appears (which has probability ), then take the $1 profit and quit. If red does not appear and you lose this bet (which has probability  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}.

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(b) Are you convinced that the strategy is indeed a “winning” strategy? Explain your answer!

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(c) Find E[X].