2. Individual Problems 17-2

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 expectedpayofffrom 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?)