In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost. One option in a roulette game is to bet $8 on red. If the ball lands on red, you get to keep the $8 you paid to play the game, and you are awarded $9. If the ball lands elsewhere, you are awarded nothing, and the $8 that you bet is collected. What is the expected value of the game?

In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost. One option in a roulette game is to bet $8 on red. If the ball lands on red, you get to keep the $8 you paid to play the game, and you are awarded $9. If the ball lands elsewhere, you are awarded nothing, and the $8 that you bet is collected. What is the expected value of the game?

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...

See similar textbooks

Related questions

Q: In roulettem, if a player uses the doubling strategy starting with a $10 bet and is betting on red…

A: Given that, Odds are one-one

Q: Suppose you are invited to play a game in which you bet $1 on any number from 000 to 599. If your…

A: Given that there are numbers from 000 and 599. That is, there are 600 numbers. If your number comes…

Q: Consider rolling a 6-sided die. The outcome of interest is the number of dots that appears on the…

A: Rolling a 6-sided die, The possible outcomes are 1,2,3,4,5,6Since each of these is equally likely,…

Q: Rafael is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized…

Q: Frank is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6.…

Q: An American roulette wheel contains 38 numbers of which 18 are red, 18 are black, and 2 are green.…

A: The odds in against of event A is (1 - P(A))/P(A).

Q: Monica is trying to design a coin-flipping game for a charity fair. The plan is for contestants to…

Q: Milan Is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized…

A: Total slices=10 2 black 4 gray 4white We have to calculate odds .

Q: 2. Suppose you're on the Las Vegas strip, and an enthusiastic stranger approaches you asking if…

A: a. For a valid probability distribution, P(X=x) ≥ 0 and Σ P(X=x) = 1

Q: Teagan is planning her university schedule. She is trying to decide between two different…

A: For the following probability,

Q: 4. Suppose John offers what he believes to be a fair bet as to whether an instructor will or will…

A: Given: Job believes there will be a quiz and offers a:b odds. He offers what he believes to be a…

Q: A game consists of rolling a die. If the die shows 6, the player wins $10. If the die shows a 3,4,5…

A: We first make a probability distribution outcome 1 2 3 4 5 6 winning amount (xi) 0 0 1 1 1 10…

Q: A game-show spinner has these odds of stopping on particular dollar values: 55% for $5, 20% for…

A: The odds of player wining $500 is 15% and the odds of player wining $1,000 is 10%.

Q: The world famous gambler from Philadelphia, Señor Rick, proposes the following game of chance: You…

A: Given Information: A fair die is rolled. If 1 is rolled, then Señor Rick pays you $20. If 2 is…

Q: has these odds of stopping on particular dollar values: 55% for $25, 20% for $100, 15% for $500, and…

A: It is given that the game show spinner has the odds of stopping the particulars dollars. $25 55%…

Q: In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting…

A: Hi! Thank you for the question, As per the honour code, we are allowed to answer three sub-parts at…

Q: The two finalists in a tennis tournament are playing for the championship. The winner will receive…

A: Given: Price of winner=60,000 Price of runner=35,000 The objective is to find the expected winnings…

Q: In strategy games, in addition to the common 6-sided dice, dice having 4, 8, 12, or 20 sides are…

A: Probability quantifies the chances of happening an event. The probability values always lie in the…

Q: Omar is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized…

A: Given data omar is at the grand opening celebration of a super market.He spins a wheel with 10 equal…

Q: The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: at a casino, you throw a fair 4 sided dice whose sides are labeled 1, 2, 3 and 4. If you land on…

A: Solution: Total number of sides in a fair dice is = 4 Sides labeled as = 1, 2, 3, 4 The…

Q: Find the odds in favor of obtaining the following outcome. a jack when drawing 1 card from an…

Q: A game-show spinner has these odds of stopping on particular dollar values: 60% for $10, 20% for…

A: Given: Odds of winning $10, P(A)=60100 Odds of winning $25, P(B)=20100 Odds of winning $100,…

Q: A modified roulette wheel has 40 slots. One slot is 0, another is 00, and the others are numbered 1…

A: Given: 40 slots numbered 0, 00 and 1 to 38

Q: Roulette. An American roulette wheel contains 38 numbers, of which 18 are red, 18 are black, and 2…

A: Odd:If the odds in favor of an event are a to b, then the probability the event occurs is a/(a+b).

Q: In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting…

A: Let's go deeper into the concepts and explanation of this problem, touching on every important…

Q: The Cyclones play Baylor on Tuesday. If the odds for the Cyclones winning are 7:2, what is the…

A: The odds for the Cyclones winning are 7:2

Q: You are playing Dungeons & Dragons with friends and have to roll 6-sided dice to decide how events…

A: We have to roll a dice and find out the odds of the given events.

Q: Please See Picture

A: X- be the winnings when we quit.Case-1 win in first spinProbability of win in first spin =…

Q: Your friend offers to place a bet with you. He will pay you$1if your favorite sports team wins the…

A: Let X be the random variable denoting the amount of money ($) you win or lose. And P(X) denotes the…

Q: A game-show spinner has these odds of stopping on particular dollar values: 55% for $5, 20% for $25,…

A: Given data: P( winning 5)=0.55 P( winning 25)=0.2 P( winning 5 or 25)=0.55+0.2=0.75

Q: A beverage company puts game pieces under the caps of its drinks and claims that one in six game…

A: Odds of the situation is the ratio of favourable cases to unfavourable cases

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

on red. If the ball lands on red, you get to keep the

you paid to play the game, and you are awarded

$9.

If the ball lands elsewhere, you are awarded nothing, and the

that you bet is collected. What is the expected value of the game?

In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost.
One option in a roulette game is to bet $8 on red. If the ball lands on red, you get to keep the $8 you paid to play the game, and you are awarded $9. If the ball lands elsewhere, you are awarded nothing, and the $8 that you bet is collected. What
is the expected value of the game?
The expected value for playing roulette if you bet $8 on red is approximately $
(Round to the nearest cent as needed.)

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Suppose you are invited to play a game in which you bet $1 on any number from 000 to 899. If your number comes up, you get $450. Find the expected winnings. Expected winnings = $ (Type an integer or decimal rounded to the nearest cent as needed.)
The world famous gambler from Philadelphia, Senior Rick, proposes the following game of chance. You roll a fair die. If you roll a 1, then Senior Rick pays you $25. If you roll a 2, Senior Rick pays you $5. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must pay Senior Rick $10, and if you roll a 6, you must pay Senior Rick $15. Is Senior Rick loco for proposing such a game? Explain and use expected values.
Suppose you are invited to play a game in which you bet $1 on any number from 000 to 599. If your number comes up, you get $300. Find the expected winnings. Expected winnings = $ (Type an integer or decimal rounded to the nearest cent as needed.)
The new england patriorts and the dallas cowboys are playing. what are the possible outcomes
A modified roulette wheel has 40 slots. One slot is 0, another is 00, and the others are numbered 1 through 38, respectively. You are placing a bet that the outcome is an even number. (In roulette, 0 and 00 are neither odd nor even.)Question content area bottomPart 1a. What is your probability of winning?The probability of winning is enter your response here.(Type an integer or a simplified fraction.)Part 2b. What are the actual odds against winning?The actual odds against winning are enter your response here:enter your response here.Part 3c. When you bet that the outcome is an even number, the payoff odds are 1:1. How much profit do you make if you bet $16 and win?If you win, the payoff is $enter your response here.Part 4d. How much profit should you make on the $16 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning?$enter your response here (Round to the nearest cent as needed.)
A game uses a single 6-sided die. To play the game, the die is rolled one time, with the following results: Even number = lose $9 1 or 3 = win $2 5 = win $10.
Tony is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random. This game is this: Tony spins the spinner once. He wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner stops on the number 3, and $7 if the spinner stops on the number 4. He loses $8 if the spinner stops on 5 or 6. (a) Find the expected value of playing the game. dollars (b) What can Tony expect in the long run, after playing the game many times? O Tony can expect to gain money. He can expect to win dollars per spin. O Tony can expect to lose money. He can expect to lose dollars per spin. O Tony can expect to break even (neither gain nor lose money). S ?
A local community group is holding a charity carnival to build a new playground. The organizers have created a dice game that they call Slam and a card game that they call Snap. The odds against winning Slam are 5:2, and the odds against winning Snap are 8:3. If kids considered their odds, which game would you recommend they play? (Show your work.)
Suppose you are playing a game where you bet $5 and have a 48% chance of winning. The bet is 1:1. What is the house edge on a single game?
you roll two standard dice. If you roll doubles, then you pay $5. If the game is fair, what would the house have to pay if you do not roll doubles?
Lisa is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random. This game is this: Lisa spins the spinner once. She wins $1 if the spinner stops on the number 1, $4 if the spinner stops on the number 2, $7 if the spinner stops on the number 3, and $10 if the spinner stops on the number 4. She loses $11 if the spinner stops on 5 or 6. (a) Find the expected value of playing the game. | dollars (b) What can Lisa expect in the long run, after playing the game many times? O Lisa can expect to gain money. She can expect to win dollars per spin. O Lisa can expect to lose money. She can expect to lose dollars per spin. O Lisa can expect to break even (neither gain nor lose money).
the carnival has come to town, and lucky louie has once again set up his pavilion. He offers a simple game consisting of rolling two normal six-sided dice at the same time for the extraordinarily low price of $3.00 per play. If the player rolls a sum of 3, the player wins $13.00; if the sum is a 9, the player wins $9.00; and if the sum is a 12, the player wins $12.00. Otherwise, the player does not win anything. How much should you expect to win or lose per game (after paying the $3.00) ?