You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is. Given that this is ________ (POSITIVE/NEGATIVE), you (SHOULD/ SHOULD NOT) play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is .(Hint: At what probability does playing the final round yield an expected value of zero?)
You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is. Given that this is ________ (POSITIVE/NEGATIVE), you (SHOULD/ SHOULD NOT) play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is .(Hint: At what probability does playing the final round yield an expected value of zero?)
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter17: Making Decisions With Uncertainty
Section: Chapter Questions
Problem 17.2IP
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Question
![You're a contestant on a TV game show. In the final round of the game, if contestants answer a
question correctly, they will increase their current winnings of $3 million to $4 million. If they are
wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the
question correctly.
Ignoring your current winnings, your expected payoff from playing the final round of the game show
is. Given that this is ______________ (POSITIVE/NEGATIVE), you___________ (SHOULD/ SHOULD NOT)
play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.)
The lowest probability of a correct guess that would make the guessing in the final round profitable (in
expected value) is
(Hint: At what probability does playing the final round yield an
expected value of zero?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe78de650-7df4-43c9-ac37-36f21892f827%2Fe6029843-9ada-4b3e-9e45-d9ebcf0b720c%2Fc5i42ld_processed.png&w=3840&q=75)
Transcribed Image Text:You're a contestant on a TV game show. In the final round of the game, if contestants answer a
question correctly, they will increase their current winnings of $3 million to $4 million. If they are
wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the
question correctly.
Ignoring your current winnings, your expected payoff from playing the final round of the game show
is. Given that this is ______________ (POSITIVE/NEGATIVE), you___________ (SHOULD/ SHOULD NOT)
play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.)
The lowest probability of a correct guess that would make the guessing in the final round profitable (in
expected value) is
(Hint: At what probability does playing the final round yield an
expected value of zero?)
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