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Monopoly is “the most played board game in the world,” according to Hasbro, its manufacturer. Players take turns moving around the board, according to a roll of a pair of dice. The board consists of
This game can be analyzed by using Markov chains. There are
HINT: The probabilities of moving from “Go” to Mediterranean Avenue, Community Chest, Baltic Avenue, Income Tax, Reading Railroad, or Oriental Avenue are each
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Chapter 11 Solutions
EBK MATHEMATICS: A PRACTICAL ODYSSEY
- 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 8 spots labeled $1, 16 spots labeled $2, and 1 spots labeled $10, how much should a player expect to win on average?arrow_forwarda pair of dice is rolled once. Suppose that you lose 9$ if the dice sum to 5 and win 10$ if the dice sum to 11 or 8. How much should you win or lose if any other number turns up in order for the game to be fair?arrow_forwardMickey and Minnie are playing a game. They spin a spinner that has 11 equally sized pieces, 3 red, 2 blue, 1 green and 5 yellow. If the spinner lands on yellow, Minnie wins $7. If it lands on blue, Minnie wins $ 4. If it lands on any other section, Minnie loses money. In order for the game to be fair, Minnie must lose $ Blank 1. Calculate the answer by read surrounding text. ifarrow_forward
- The new england patriorts and the dallas cowboys are playing. what are the possible outcomesarrow_forwardXYZ company has designed a new lottery scratch-off game. The player is instructed to scratch off one spot: A, B, or C. A can reveal "loser," "win $1," or "win $50." B can reveal "loser" or "take a second chance." C can reveal "loser," or "win $500." On the second chance, the player is instructed to scratch off D or E. D can reveal "loser" or "win $1." E can reveal "loser" or "win $10." The probabilities at A are 0.9, 0.09, and 0.01 respectively. The probabilities at B are 0.8 and 0.2. The probabilities at Care 0.999 and 0.001. The probabilities at D are 0.95 and 0.05. The probabilities at E are 0.5 and 0.5. Calculate the expected value of the game and provide recommendations to a decision-makerarrow_forwardA technology store holds a contest to attract shoppers. works: An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn over cards one at a time, looking for the ace. The person wins $100 of store credit if the ace is the first card, $50 if it is the second card, and $20, $10, or $5 if it is the third, fourth, or last card chosen. What is the average dollar amount of store credit given away in the contest? Estimate with a simulation of 10 trials. Once an hour, someone at checkout is chosen at random to play in the contest Here's how it 67819 00354 91439 91073 49258 15992 41277 75111 67496 68430 09875 08990 27656 15871 23637 00952 97818 64234 50199 05715arrow_forward
- 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?arrow_forwardYou go to a casino and play a game. You throw a fair 4 sided die whose sides are labeled 1, 2, 3 and 4. If you land on a 1, you get $30. If you land on a 2, you get $10. If you land on either a 3 or a 4, you owe the casino $8. If you play this game repeatedly, what would your "winnings" be on average, in dollars?arrow_forwardYou 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?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 $-1.5 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_forwardyou 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?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_forward
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