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You roll a die. If it comes up a 6, you win $200. If not, you get to roll again. If you get a 6 the second time, you win $100. If not, you lose. a) Create a probability model for the amount you win. b) Find the expected amount you'll win. c) What should you be willing to pay to play this game?

You roll a die. If it comes up a 6, you win $200. If not, you get to roll again. If you get a 6 the second time, you win $100. If not, you lose. a) Create a probability model for the amount you win. b) Find the expected amount you'll win. c) What should you be willing to pay to play this game?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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You roll a die. If it comes up a 6, you win $200. If not, you get to roll again. If you get a 6 the second time, you win $100. If not, you lose. a) Create a probability model for the amount you win. b) Find the expected amount you'll win. c) What should you be willing to pay to play this game? a) Amount won P(Amount won) $0 $100 $200 (Type integers or simplified fractions.) b) The expected amount you'll win is $ (Round to two decimal places as needed.) c) What should you be willing to pay to play this game? O A. As much as possible, because the game has good odds and the payout is proportional to the wager. O B. Exactly the expected value, because the probability of profiting decreases for larger wagers and the payout decreases for smaller wagers. O C. No more than the expected value, because this is the average payout of the game. O D. No more than half of the expected value, because this gives a 50% chance of profiting.
Transcribed Image Text:You roll a die. If it comes up a 6, you win $200. If not, you get to roll again. If you get a 6 the second time, you win $100. If not, you lose. a) Create a probability model for the amount you win. b) Find the expected amount you'll win. c) What should you be willing to pay to play this game? a) Amount won P(Amount won) $0 $100 $200 (Type integers or simplified fractions.) b) The expected amount you'll win is $ (Round to two decimal places as needed.) c) What should you be willing to pay to play this game? O A. As much as possible, because the game has good odds and the payout is proportional to the wager. O B. Exactly the expected value, because the probability of profiting decreases for larger wagers and the payout decreases for smaller wagers. O C. No more than the expected value, because this is the average payout of the game. O D. No more than half of the expected value, because this gives a 50% chance of profiting.
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