- #1

penguinnnnnx5

- 36

- 0

## Homework Statement

Here are the problems:

A roulette wheel has 38 slots, numbered 0, 00, and 1 through 36. If you bet 1 on a speciﬁed number, you either

win 35 if the roulette ball lands on that number or lose 1 if it does not. If you continually make such bets, approximate the probability that

a. you are winning after 34 bets;

b. you are winning after 1,000 bets;

c. you are winning after 100,000 bets.

## Homework Equations

(X - np) / sqrt(np(1-p))

## The Attempt at a Solution

So I've tried to implement the central limit theorem with binomial properties.

n = 1000, p = 1/38, X = 500 based on an example from the lecture slides here and here

However, when I plug everything in, everything is way too high as shown:

(500 - 1000/38) / √(1000/38 * 37 / 38) = 93.57775

Since they are so high, I cannot use this normal distribution table I was provided.

I have no idea how to do these types of problems. If anyone can please kindly explain to me the process, it would be very helpful and I will be very grateful. You don't even have to tell me the answer, or you can only do one of the questions as an example. I just want to know how it's done please.