o raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $ (c) Is this game fair? Yes No

o raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $ (c) Is this game fair? Yes No

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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To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $23. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) -8 9/32 Yes No (c) Is this game fair? 1 12/32 (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $2.93 14 Enter a fraction, integer, or exact decimal. Do not approximate. 11/32
To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $4 to play. The game works as follows: A fair 4-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, and orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $25. If the die shows an even number and the spinner does not show orange, then you win $10. Otherwise, you don't win anything. Let X be your net winnings. a. Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) b. Compute your expected net winnings for the game. Round your answer to the nearest cent. $ c. Is this game fair?
To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $5 to play. The game works as follows: A fair 10-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, and orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $24. If the die shows an even number and the spinner does not show Otherwise you don't win anything. orange, then you win $12. Let X be your net winnings. a. Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. Р(X) b. Compute your expected net winnings for the game. Round your answer to the nearest cent. 2$ c. Is this game fair? ?
Jane draws a marble from a box containing 5 red marbles, 3 green marbles, and4 blue marbles. She receives $2 for a red marble and $3 for a green marble that she draws.If she draws a blue marble, she loses $4. Is the game fair? How many dollars should Janepay for a draw in a fair game?
The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $35. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 717 cookies before the drawing. Lisa bought 31 cookies. What is the probability she will win the dinner for two? Write your answer as a fraction in the simplest form, if one exists. A. 31/686 B. 686/717 C. 31/717 D. 1/31 E. none of these choices
A man went to Atlantic City with $2000 and placed 100 bets of $20 each, one after another, on the same number on the roulette wheel. There are 38 numbers on the wheel, and the gaming casino pays 35 times the amount bet if the ball drops into the bettor’s numbered slot in the roulette wheel. In addition, the bettor receives back the original $20 bet. Estimate how much money the man is expected to win or lose in Atlantic City.
A restaurant hands out a scratch-off game ticket with prizes being worth purchases at the restaurant.
The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $39. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 720 cookies before the drawing. Lisa bought 32 cookies. What is the probability she will not win the dinner for two? Write your answer as a fraction in the simplest form, if one exists. A. 2/43 B. 43/45 C. 2/45 D. 1/32 E. none of these
The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of the dinner for two at a local Chinese restaurant. The dinner is valued at $35. Since the fortune cookies were donated to the club, we can ignore the cost of the cookies. The club sold 571 cookies before the drawing. (a) Lisa bought 14 cookies. What is the probability she will win the dinner for two? (Round your answer to three decimal places.)
The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $37. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 27 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. How much did she effectively contribute to the hiking club? A. $23.55 B. $49.41 C. $52.61 D. $25.63 E. $25.61
The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $34. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 721 cookies before the drawing. Lisa bought 17 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.
You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $60; otherwise, you lose $3. What is the price that you should pay to play the game that would make the game fair?