A roulette wheel has 38 slots and a ball that rolls until it falls into one of the slots, all of which are equally likely. Eighteen slots are black numbers, eighteen are red numbers, and two are green zeros. If you bet on “red,” and the ball lands in a red slot, the casino pays you your bet (i.e. you get your twice your money back); otherwise, the casino wins your bet. (a) What is the expected value of a $1 bet on red? (b) Suppose you bet $1 on red, and if you win you "let it ride" and bet $2 on red. What is the expected value of this plan? (c) Suppose you bet $1 on red, and if you win you "bet your winnings" and again bet $1 on red. What is the expected value of this plan?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question
A roulette wheel has 38 slots and a ball that rolls until it falls into one of the slots, all of which are equally likely. Eighteen slots are black numbers, eighteen are red numbers, and two are green zeros. If you bet on “red,” and the ball lands in a red slot, the casino pays you your bet (i.e. you get twice your money back); otherwise, the casino wins your bet.

(a) What is the expected value of a $1 bet on red?

(b) Suppose you bet $1 on red, and if you win you “let it ride” and bet $2 on red. What is the expected value of this plan?

(c) Suppose you bet $1 on red, and if you win you “bet your winnings” and again bet $1 on red. What is the expected value of this plan?
Transcribed Image Text:A roulette wheel has 38 slots and a ball that rolls until it falls into one of the slots, all of which are equally likely. Eighteen slots are black numbers, eighteen are red numbers, and two are green zeros. If you bet on “red,” and the ball lands in a red slot, the casino pays you your bet (i.e. you get twice your money back); otherwise, the casino wins your bet. (a) What is the expected value of a $1 bet on red? (b) Suppose you bet $1 on red, and if you win you “let it ride” and bet $2 on red. What is the expected value of this plan? (c) Suppose you bet $1 on red, and if you win you “bet your winnings” and again bet $1 on red. What is the expected value of this plan?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 4 images

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON