Question

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 $1,500,000. You believe you have a 50% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is S . Given that this is play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) you (Hint: At The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is what probability does playing the final round yield an expected value of zero?)

Answer 1

So expected payoff will be =

0.5(4) + 0.5(1.5) = 2.75 million

Hence as we can see that this is less than the current winnings i.e 3 million we will not take the risk and will not play the final round

In order to make us play it our current winning should be equal to expected payoff from final round.

So, finding the probability of playing

4p + 1.5(1-p) = 3

4p + 1.5 - 1.5p = 3

2.5p = 1.5

p = 0.6

Hence the lowest probability must be 60%