Question 725116
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.