(b) A Roulette table has numbers from 0 to 36 to place bets on. 18 of them red, 18 of them are black, and one of them is green. In every round, one of the numbers between 0 and 36 is randomly chosen to win. You can place a bet on a single number, or you can place a bet on all red numbers simultaneously. If you place $1 on red and a red number is chosen, you double your money, otherwise you lose your money. If you place $1 on a single number and this number is chosen, you get back $36 (including the $1 you placed), otherwise you lose your money. (i) Calculate the expected value for the money you win if you place $1 on red. What is the expected value for the money you win if you place $1 on a single number? Show all your working. (ii) How much money can you expect to end up with, if you start out with $37 and you place $1 on red 37 times in a row? Justify your answer. (iii) Assume you start with $10 and you place $1 on a single number 10 times in a row. Calculate the probability that you lose all of your money. What is the probability that you win exactly once? Show all your working and justify your answers.
(b) A Roulette table has numbers from 0 to 36 to place bets on. 18 of them red, 18 of them are black, and one of them is green. In every round, one of the numbers between 0 and 36 is randomly chosen to win. You can place a bet on a single number, or you can place a bet on all red numbers simultaneously. If you place $1 on red and a red number is chosen, you double your money, otherwise you lose your money. If you place $1 on a single number and this number is chosen, you get back $36 (including the $1 you placed), otherwise you lose your money. (i) Calculate the expected value for the money you win if you place $1 on red. What is the expected value for the money you win if you place $1 on a single number? Show all your working. (ii) How much money can you expect to end up with, if you start out with $37 and you place $1 on red 37 times in a row? Justify your answer. (iii) Assume you start with $10 and you place $1 on a single number 10 times in a row. Calculate the probability that you lose all of your money. What is the probability that you win exactly once? Show all your working and justify your answers.
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...
Related questions
Question

Transcribed Image Text:(b) A Roulette table has numbers from 0 to 36 to place bets on. 18 of them red, 18 of them are black,
and one of them is green. In every round, one of the numbers between 0 and 36 is randomly chosen to
win. You can place a bet on a single number, or you can place a bet on all red numbers simultaneously. If
you place $1 on red and a red number is chosen, you double your money, otherwise you lose your
money. If you place $1 on a single number and this number is chosen, you get back $36 (including the $1
you placed), otherwise you lose your money.
(i) Calculate the expected value for the money you win if you place $1 on red. What is the expected
value for the money you win if you place $1 on a single number? Show all your working.
(ii) How much money can you expect to end up with, if you start out with $37 and you place $1 on red
37 times in a row? Justify your answer.
(iii) Assume you start with $10 and you place $1 on a single number 10 times in a row. Calculate the
probability that you lose all of your money. What is the probability that you win exactly once? Show
all your working and justify your answers.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps

Recommended textbooks for you

A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON


A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
