Concept explainers
Suppose someone was playing the following dice game. The game costs
a. What is the expected value of this game, taking into consideration the
b. Does the game favor you, or the people who play it?
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A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
- A pair of fair dice is rolled once. Suppose that you lose $11 if the dice sum to 3 and win $12 if the dice sum to 10 or 2. How much should you win or lose if any other number turns up in order for the game to be fair? To keep the game fair, you should 2$ if the dice sum to any other number. (Do not round until the final answer. Then round to the nearest cent as needed.)arrow_forwardYou play a game with two six-sided dice. If you roll a sum of 3 or 8 you win ₱600 and if you roll a sum of 10,you win ₱400. However, you lose ₱500 if you roll for anything else. If you continue to play the game, howmuch do you expect to win or lose in the game? Show complete solution.arrow_forwardYou need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $5 if the spinner lands on blue and $15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?arrow_forward
- This game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…arrow_forwardThis game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…arrow_forwardA pair of fair dice is rolled once. Suppose that you lose $8 if the dice sum to 7and win $13if the dice sum to 4 or 8.How much should you win or lose if any other number turns up in order for the game to be fair?arrow_forward
- 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 $-1.50). If you roll a 4 or 5, you win $3.50 (i.e., your net profit is $2.00). If you roll a 6 you win $5.00 (i.e., your net profit is $3.50).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) 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=arrow_forwardSuppose 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=arrow_forwardSuppose 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.arrow_forward
- Suppose you play a game where you roll 2 six-sided dice. If you roll a 7, you will lose some money, but if you roll anything else you will win 100. How much money would you have to lose in order for you average 0 per roll?arrow_forwardSuppose 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=arrow_forwardIn this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game. = Win a prize = Do not win a prize 1. Start by determining the probabilities for winning a prize and not winning a prize. Draw a probability tree to find the possible outcomes and the probabilities. After you draw the tree, check you work by clicking on the link below. Click to hide hint CHIP 1 CHIP 2 Probability P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25 0.5 0.5 0.5 P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25 Start 0.5 0.5 P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25 0.5 P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL