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 $1,500,000. You believe you have a 50% chance of answering the question correctly.

1)Ignoring your current winnings, your expected payofffrom playing the final round of the game show is $ ?

2)Given that this is either positive or negative, you either should play or not play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.)

3)The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is either 42% or 60% or 63% or 66%?

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