A gambling book recommends the following "winning strategy"for the
game of roulette. It recommends that a gambler bet $1 onred. If red
appears (which has probablity 18/38), then the gamblershould take
her $1 profit and quit. If the gambler loses this bet(which has
probablity 20/38 of occurring), she should makeadditional $1 bets
on red on each of the next two spins of theroulette wheel and then
quite. Let X denote the gambler's winningswhen she quites.


(a) Find P{X > 0}.

(b) Are you concinved that the strategy is indeed a
"winning"strategy? Explain your answer.

(c) Find E[X].