3. Consider the following game: Two fair, six-sided dice is rolled. If the numbers rolled do not match, you lose one dollar. If you roll an even double you win one dollar and if you roll an odd double you win six dollars. (a) Let x be the discrete random variable representing the amount of money won in a given roll. Define the probability distribution of x, p(x). (b) What is the mean, or expected value, of x? Interpret your results in terms of how you will fair playing the game in the long-run. (c) What is the standard deviation of x? (d) Now consider changing the amount of money won in the event of rolling an even double. What amount of money would ensure that in the long-run you break even?

3. Consider the following game: Two fair, six-sided dice is rolled. If the numbers rolled do not match, you lose one dollar. If you roll an even double you win one dollar and if you roll an odd double you win six dollars. (a) Let x be the discrete random variable representing the amount of money won in a given roll. Define the probability distribution of x, p(x). (b) What is the mean, or expected value, of x? Interpret your results in terms of how you will fair playing the game in the long-run. (c) What is the standard deviation of x? (d) Now consider changing the amount of money won in the event of rolling an even double. What amount of money would ensure that in the long-run you break even?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section: Chapter Questions

Problem 3P: Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the...

See similar textbooks

Similar questions

You toss two six-sided dice. What is the probability that the total of the two dice is 5?
A manufacturer has determined that a machine averages one faulty unit for every 500 it produces. What is the probability that an order of 300 units will have one or more faulty units?
Sick leave probability that a given worker at Dyno Nutrition Will call in sick on a Monday is 004. The packaging department has eight workers. What is the probability that two or more ackaging workers Will call in sick next Monday ?
Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an $8000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning (and that of B winning) if the game were to continue? The French mathematicians Pascal and Fermat corresponded about this problem, and both came to the same correct conclusion (though by very different reasoning's). Their friend Roberval disagreed with both of them. He argued that player A has probability of Winning, because the game can end in the four ways H, TH, TTH, TTT, and in three of these, A wins. Roberval’s reasoning was wrong. Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform this experiment 80 or more times, and estimate the probability that player A wins. Calculate the probability that player A wins. Compare with your estimate from part (a).