Question 872573: In a TV game show, 4 prizes are hidden on a game board that contains 20 spaces.
One prize is worth $10,000, two prizes are worth $5,000 each, and one prize is
worth $1,000, with the remaining spaces containing no prize. The show's host
offers a contestant their choice of $1,000 (for not playing) or the opportunity to select one space on the game board. How much greater is the expected value of picking a space on the board than not playing the game? I think I got it figured out but I'm still not sure.
A.$50
B.$100
C.$1,000
D.$4,500
E. The expected value is greater for not playing the game than it is for playing it.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a TV game show, 4 prizes are hidden on a game board that contains 20 spaces.
One prize is worth $10,000, two prizes are worth $5,000 each, and one prize is
worth $1,000, with the remaining spaces containing no prize. The show's host
offers a contestant their choice of $1,000 (for not playing) or the opportunity to select one space on the game board. How much greater is the expected value of picking a space on the board than not playing the game? I think I got it figured out but I'm still not sure.
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Random "win" values...... 10,000......5000....1000....0
Probabilities.............1/20.......2/20.....1.20...16/20
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Expected "win" value = [10,000 + 2*5000 + 1000)/20 = 21000/20 = $1050
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Answer:: $50
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Cheers,
Stan H.
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A.$50
B.$100
C.$1,000
D.$4,500
E. The expected value is greater for not playing the game than it is for playing it.
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