We all dream of winning big, becoming an instant millionaire; but how likely is
ID: 3205051 • Letter: W
Question
We all dream of winning big, becoming an instant millionaire; but how likely is that? Let's say we decide to pursue our goal of winning big money by going to a casino and continually playing what we think will be an easy game: roulette. Can we expect to win big in the long run? Is one bet better than another? How do the casinos make so much money anyway? If we are betting against the casino, how do they make sure that they always win? This project will help you answer these questions. Let's begin with a lesson in roulette. Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Halfofthe numbers 1-36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. We can make many different types of bets, but two ofthe most common are to beton a single number (1-36) or to bet on a color (either red or black. These will be the two bets we will consider in this project. After all players place their bets on the table, the wheel is spun and the ball tossed onto the wheel. The pocket in which the ball lands on the wheel determines the winning number and color. The ball can land on only one color and number at a time. We begin by placing a bet on a number between 1 and 36. This bet pays 36 to 1 in most casinos, which means we will be paid S36 for each S1 webet on the winning number. If we lose, we simply lose whatever amount of money we bet. 1. Calculate the probability that we will win on a single spin of the wheel. 2. Calculate the probability that we will lose. 3. If we bet S8 on the winning number, how much money will we win? 4. What is the expected value of a bet on a single number if we bet SI? 5. For a S5 bet, what is the expected value of a bet on a single number? 6. What is the expected value of a bet on a single number if we bet $10? 7. Do you see a pattern in the answers to the last three questions?Explanation / Answer
In a Roulette wheel, there are total 36+2 = 38 numbers available i.e. 38 possible outcomes on rotating the wheel.
As a part of bet, we are betting on any number from 1 to 36. Selecting any number from the 36 numbers can be done in 36C1 ways.
Probability of appearing any number as the outcome of the rotation is 1/38 (As there are 38 outcomes are possible)
Probability of getting a number on which bet has put is 1/38, hence the probability of wining a game in single spin is 1/38
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