Contestants are 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 $1 million to $3 million. If they are wrong, their prize is decreased to $750,000. One contestant believes they have a 25% chance of answering the question correctly.

Ignoring current winnings, the expectedpayofffrom playing the final round of the game show is $?.

Given that this is

A. Positive

B. Negative

the contestant

A. Should

B. Should not

play the final round 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

A. 11.6667%

B. 11.0000%

C. 11,1111%

D. 6.6667%

(Hint: At what probability does playing the final round yield an expected value of zero?)