# Roulette probability

One option in a roulette game is to bet $18 on red.There are 18 red compartments,18 black compartments,and 2 compartments neither red nor black.If the ball lands on red you get to keep the $18 you paid to play the game and you are awarded $18 if the ball lands elsewhere you are awarded nothing and the $18 you bet will be collected.

1.What is the expected value of playing roulette if you bet $18 on red ?

2. Which of the statements tells what this value means ?

A. Over the long run a player can expect to lose this amount in each game

B. Over the long run the player can expect to break even

C.Over the long run the player can expect to win this amount each game

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Please see the attached Word document for the solution to this exercise.

ROULETTE PROBABILITY

One option in a roulette game is to bet $18 on red. There are 18 red compartments; 18 black compartments, and 2 compartments that are neither red nor black. If the ball lands on red you get to keep the $18 you paid to play the game and you are awarded $18 if the ball lands elsewhere you are awarded nothing and the $18 you bet will be collected.

1. What is the expected value of playing roulette if you bet $18 on red?

The expected value of a discrete random variable is ...

#### Solution Summary

This provides an example of working with probability and expected value for a roulette game.

Roulette Probabilities

A success, s in Bernoulli trials is often derived from the collection of outcomes. For example, an American roulette wheel consists of 38 numbers, of which 18 are black, 18 are red, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any one of the 38 numbers. If you're interested in which number the ball lands on, each play at the roulette wheel has 38 possible outcomes. Suppose however, you're betting on red. Then you're interested only in whether the ball lands on a red number or it doesn't. Hence successive bets on red constitute a sequence of Bernoulli trials with success probability |18 divided by 38.

If four plays at a roulette wheel, what is the probability that the ball lands on red

a) Exactly twice

b) At least once

c) Determine and interpret the average times the ball lands on red