# Roulette

• Sep 21st 2009, 09:00 PM
tbl9301
Roulette
Suppose you bet a dollar on red, 25 times in a row, at roulette. Each time you win a dollar with probability 18/38, lose with probability 20/38. Find, approximately, the chance that after 25 bets you have at least as much money as you started with.

I'm not sure how you're supposed to set this up .. and would you use like the normal distribution? Please helpp :(
• Sep 22nd 2009, 04:18 AM
CaptainBlack
Quote:

Originally Posted by tbl9301
Suppose you bet a dollar on red, 25 times in a row, at roulette. Each time you win a dollar with probability 18/38, lose with probability 20/38. Find, approximately, the chance that after 25 bets you have at least as much money as you started with.

I'm not sure how you're supposed to set this up .. and would you use like the normal distribution? Please helpp :(

Suppose you win $N$ of the spins, then you have a return of:

$R(N)=\frac{18}{38}N-\frac{20}{38}(25-N)$

Now solve for $N$ the equation $R(N)=0$. If you win this number or more of the spins you have have at least as much as you started with.

The number of wins has a binomial distribution $B(25,18/38)$, you use this (or the normal approximation to this) to calculate the probability that you win at least the number of spins calculated above.

CB