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 $1 million to $3 million. If they are wrong, their prize is decreased to $750,000. 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? (6.67%, 11.67%, 11%, 11.11%) .

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

Answer 1

1. Tou have a 25% chance of winning $2 million but you also have a 75% chance of losing $250,000.

Expected value = (0.25)(2,00,000) + (0.75)(-250,000)

= 500,000 - 187,500

= 312,500

Your expected payoff from playing the final round of the game show is $312,500

2. Given that this is positive, you should play the final round of the game.

3. Let x be the lowest probability of a correct guess that would make the guessing in the final round profitable.

Thus, expected value= 2000,000x - 250,000(1-x) = 0

On solving, x = 1/9

Therefore, the lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is 11.1111%