Concept explainers
Suppose you invented a game based on taking the sum of two dice. You decide the game will cost
a. What is the expected value?
b. Whom does the game favor?
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A PROBLEM SOLVING APPROACH TO MATHEMATI
- 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 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_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 $-1.50). 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_forward
- 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=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_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
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