17-2 Game Show Uncertainty In the final round of a TV game show, contestants hav
ID: 1097006 • Letter: 1
Question
17-2 Game Show Uncertainty
In the final round of a TV game show, contestants have a chance to increase their current winnings of 1 million dollars to 10 million dollars. If they are wrong, their prize is decreased to $100,000. To win, they have to guess the exact percentage that answered a question a certain way, and the range has already been narrowed to an 11-point range. So, for example, the contestant knows that the correct answer is between 20% and 30% and he or she must guess the correct percentage in that range. So, let
Explanation / Answer
Answer.
Probability of winning a game is = 1/11
Probability of losing a game is = 10/11
His expected value = 1/11 * 10 million + 10/11 * 0.1 million
= (10 + 1)million/11
= 1 million
Hence the expected value is same as the certain value that he is getting without playing a game.
Hence if the person is risk averse, He should not play the game
But if the person is risk lover, He should play the game.