In the casino game of American roulette, the wheel is divided into 38 compartments numbered 1 through 36, 0, and 00. One-half of the numbers 1 through 36 are red, the other half black, and 0 and 00 are green. Of the many types of bets that may be placed, one type involves betting on the outcome of the color of the winning number. For example, one may place a certain sum of money on red. If the winning number is red, one wins an amount equal to the bet placed and the amount of the bet is returned; otherwise, one loses the amount of the bet. If a player placed a $95 bet on red and a $95 bet on black in a single play in American roulette, what would be the expected value of his winnings? (Round your answer to the nearest cent.) $

In the casino game of American roulette, the wheel is divided into 38 compartments numbered 1 through 36, 0, and 00. One-half of the numbers 1 through 36 are red, the other half black, and 0 and 00 are green. Of the many types of bets that may be placed, one type involves betting on the outcome of the color of the winning number. For example, one may place a certain sum of money on red. If the winning number is red, one wins an amount equal to the bet placed and the amount of the bet is returned; otherwise, one loses the amount of the bet. If a player placed a $95 bet on red and a $95 bet on black in a single play in American roulette, what would be the expected value of his winnings? (Round your answer to the nearest cent.) $

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Description: In the casino game of American roulette, the wheel is divided into 38 compartments numbered 1 through 36, 0, and 00. One-half of the numbers 1 through 36 are red, the other half black, and 0 and 00 are green. Of the many types of bets that may be pla

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...

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In the casino game of American roulette, the wheel is divided into 38 compartments numbered 1 through 36, 0, and 00. One-half of the numbers 1 through 36 are red, the other half black, and 0 and 00 are green. Of the many types of bets that may be placed, one type involves betting on the outcome of the color of the winning number. For example, one may place a certain sum of money on red. If the winning number is red, one wins an amount equal to the bet placed and the amount of the bet is returned; otherwise, one loses the amount of the bet.If a player placed a $85 bet on red and a $85 bet on black in a single play in American roulette, what would be the expected value of his winnings? (Round your answer to the nearest cent.)
Suppose you decided to play a gambling game. In order to play the game there is a $1.50 dollar fee to play. If you roll a 1, 2, or 3 you win nothing (i.e., your net profit is $-1.5 dollars). If you roll a 4 or 5, you win $2.50 (i.e., your net profit is $1). If you roll a 6 you win $5.75 (i.e., your net profit is $4.25).a) Use the information described above to constuct a probability distribution table for the random variable xx which represents the net profit of your winnings. Note: Be sure to enter your probabilities as reduced fractions. xx P(x)P(x) (You roll a 1,2,or 3) (You roll a 1,2, or 3) (You roll a 4 or 5) (You roll a 4 or 5) (You roll a 6) (You roll a 6) b) Find the amount you would expect to win or lose each time you played the game. Round your final answer to two decimal places.μ=
Suppose you decided to play a gambling game. In order to play the game there is a $1.00 dollar fee to play. If you roll a 1, 2, or 3 you win nothing (i.e., your net profit is $-1.00). If you roll a 4 or 5, you win $2.50 (i.e., your net profit is $1.50). If you roll a 6 you win $4.00 (i.e., your net profit is $3.00).Use the information described above to construct a probability distribution table for the random variable xx which represents the net profit of your winnings. Note: Be sure to enter your probabilities as reduced fractions. Die Roll xx P(x)P(x) Roll a 1, 2, or 3 Roll a 4 or 5 Roll a 6 Find the amount you would expect to win or lose each time you played the game. Round your final answer to two decimal places.μ=
Suppose that you and a friend are playing cards and decide to make a bet. If you draw three twos in succession from a standard deck of 52 cards without replacement, you win $100. Otherwise, you pay your friend $10. If the same bet was made 25 times, how much would you expect to win or lose?
The game of American roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money. Suppose you bet $9 on red. What's the expected value and standard deviation of your winnings?
You are on a TV show. You have been asked to either play a dice game four times or accept a $50 bill. The dice game works like this: If you roll a 1, 2, you lose $30. If you roll a 3, 4 or 5, you win $100. If you roll a 6, you lose $50. Should you play the game? Answer yes or no.
Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws two spades in succession from a standard deck of 52 cards replacing the first card, you give him $⁢50. Otherwise, he pays you $⁢10. If the same bet was made 30 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 19 spots labeled $1, 14 spots labeled $2, and 5 spots labeled $10, how much should a player expect to win on average?
Hadey is running a game of chance to raise money for a trip to Jamaica to visit his grandparents. A player pays $5 and then rolls a six-sided die. The faces of the die are different colors, one red, one blue, one yellow, one green, one purple and one orange. If the die comes up green, Hadey pays the player $20. Old Billie plays the game 120 times and loses $300. She doesn't trust Hadey and asks Letecia to test the die that Hadey is using for bias. Letecia rolls the die 600 times with the following results. yellow Red blue green 73 purple Orange 99 107 104 108 109 Perform the appropriate hypothesis test at the 0.05 significance level to determine if the die is balanced.
Your friend offers to place a bet with you. He will pay you $2 if your favorite sports team wins the game on Tuesday night. But you will pay him $3 if his team wins. Your team has an 60% chance of winning, whereas his only has a 40% chance. This bet is in your favor. True or False.
James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel. -if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000 let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23 u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053 FILL IN THE BLANK if you play 2500 times, and Let, x (x bar)= the mean winnings (or…
at a casino, you throw a fair 4 sided dice whose sides are labeled 1, 2, 3 and 4. If you land on a one, you get thirty dollars. If you land on a two, you get ten dollars. If you land on either a three or four, you owe the casino eight dollars. If you repeatedly play this game, what would your "winnings" be on average, in dollars?