Exercise 1. American Roulette probability of winning money

The exercises in the previous chapter explored winnings in American roulette. In this chapter of exercises, we will continue with the roulette example and add in the Central Limit Theorem.

In the previous chapter of exercises, you created a random variable \(S\) that is the sum of your winnings after betting on green a number of times in American Roulette.

What is the probability that you end up winning money if you bet on green 100 times?

This exercise is part of the course

HarvardX Data Science - Probability (PH125.3x)

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Exercise instructions

Execute the sample code to determine the expected value avg and standard error se as you have done in previous exercises.
Use the pnorm function to determine the probability of winning money.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Assign a variable `p_green` as the probability of the ball landing in a green pocket
p_green <- 2 / 38

# Assign a variable `p_not_green` as the probability of the ball not landing in a green pocket
p_not_green <- 1-p_green

# Define the number of bets using the variable 'n'
n <- 100

# Calculate 'avg', the expected outcome of 100 spins if you win $17 when the ball lands on green and you lose $1 when the ball doesn't land on green
avg <- n * (17*p_green + -1*p_not_green)

# Compute 'se', the standard error of the sum of 100 outcomes
se <- sqrt(n) * (17 - -1)*sqrt(p_green*p_not_green)

# Using the expected value 'avg' and standard error 'se', compute the probability that you win money betting on green 100 times.

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