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24 February, 02:41

A gambling book recommends the following "winnin strategy" for the game of roulette:

It recommends that the gambler bet $1 on red. If red appears (this has probability

18/38), then the gambler should take her $1 profit and quit. Else, 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}.

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  1. 24 February, 02:42
    0
    0.854 (85.4%)

    Step-by-step explanation:

    Since each bet is independent from others, then for X=gambler's winnings when she quits

    P (X>0) = probability to win in the first bet + probability of losing in the first bet * probability of wining at least one of the 2 additional bets

    = 18/38 + (1-18/38) * [18/38 * (1-18/38) + (1-18/38) * 18/38+18/38*18/38 ] = 0.854 (85.4%)
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