Question 725116: I have an extra credit problem that I really need the points for. Please help me!!
A student is taking a test with several multiple choice questions. One (1) point is given for each correct.If there are 4 options for each question, and the student is penalized 1/2 point for each question wrong, how many options must he be able to rule out before the expected value of guessing is zero?
?????? Must write out work for credit.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A student is taking a test with several multiple choice questions.
One (1) point is given for each correct.
If there are 4 options for each question, and the student is penalized 1/2 point for each question wrong, how many options must he be able to rule out before the expected value of guessing is zero?
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Random Values:.......1......-1/2
Probabilities:.......x.....(1-x)
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Solve:
E(x) = x - (1/2)(1-x) = 0
x - (1/2) + (1/2)x = 0
(3/2)x = 1/2
x = (2/3)(1/2) = 1/3
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So, if the probability of getting each problem correct is
1/3, expected value will be zero.
So, the student must rule out one of the options.
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Cheers,
Stan H.
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