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}.

Question

Mathematics

Alonzo Matthews

18 March, 02:12

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}.

+1

Answers (1)

Know the Answer?

Shiloh Burgess · Answer 1

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%)