# Answer to Question #8458 in Statistics and Probability for Rahul Sud

Question #8458
2. In roulette, the wheel contains 38 numbers. You pick a number, and the dealer spins the wheel. If the roulette ball lands on your number, you win. a. What is the probability that you win on the 13th try? b. Let&rsquo;s say you bet 2 \$ for every try, and make 10\$ when you win. What is the probability that in 20 tries you don&rsquo;t lose money?
In roulette, the wheel contains 38 numbers. You pick a number, and the dealer spins the wheel. If the roulette ball lands on your number, you win.
a. What is the probability that you win on the 13th try?

& P(win) = 1/38;
& P(win on the 13th try) =
& = (win or loose on the& 1st try)*
& *(win or loose on the& 2nd try)* ...
...*(win or loose on the 12th try)*
& *(win on the 13th try) =
= 1^12 * (1/38) =
= 1/38.

If the question alludes that the first 12 attemptions were unsuccessful, then

& P(loose) = 1 - 1/38 = 37/38;
& P(win on the 13th try) =
& = (loose on the& 1st try)*
& *(loose on the& 2nd try)* ...
...*(loose on the 12th try)*
& *(win on the 13th try) =
= (37/38)^12 * (1/38) =
= 223/11670 &asymp; 0.019.

b. Let&rsquo;s say you bet 2 \$ for every try, and make 10\$ when you win. What is the probability that in 20 tries you don&rsquo;t lose money?

You&#039;ll not lose money if you win at least 4 times: 4*\$10 - (20-4)*\$2 = \$8. So,

P(20 tries you don&rsquo;t lose money) = P(win at least 4 times) = (1/38)^4.

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