A student is taking a standardized test consisting of several multiple-choice questions. One point is awarded for each correct answer. Questions left blank neither receive nor lose points. There are five options for each question and the student is penalized one tenth 1/10 point for each wrong answer. Is it in the student's best interest to guess? Explain.
P(Answer is correct) = 1/5 = 0.20
P(Answer is wrong) = 1 - 0.20 = 0.80
Marks awarded for correct answer = 1
Marks deducted for wrong answer = 1/10 = 0.10
Marks (x) | P(x) | x*P(x) |
1 | 0.20 | 1*0.20 = 0.20 |
-0.10 | 0.80 | -0.10*0.80 = -0.08 |
Expected Marks = Σx*P(x) = 0.20-0.08
Expected Marks = 0.12
Since the expected value is positive, it is in the student's best interest to guess.
A student is taking a standardized test consisting of several multiple-choice questions. One point is awarded...
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