Question

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}.

Answer 1

0.854 (85.4%)

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%)