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

Question

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’s say you bet 2 $ for every try, and make 10$ when you win. What is the probability that in 20 tries you don’t lose money?

Answer 1

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 ≈ 0.019.

b. Let’s say you bet 2 $ for every try, and make 10$ when you win. What is the probability that in 20 tries you don’t lose money?

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

P(20 tries you don’t lose money) = P(win at least 4 times) = (1/38)^4.