Type your question here In the final round of a TV game show, contestants have a
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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%-30% and he or she must guess the correct percentage in that range. So, let's say you have no idea what the right answer is and have to make a random guess. Should you play?<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
Explanation / Answer
P(winning) = 11/100 = 0.11
Now, let us assume the person answers the question. His expected earning then is:
E = Amount_Earned_in_correct_answer x P(winning) + Amount_Earned_in_wrong_answer x P(losing) = $10,000,000 x 0.11 + $100,000 x 0.89 = 1,189,000
If the person does not play, he goes back with $1,000,000
Since the expected earninng is more if he answers the question, the person should make a guess.
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