Question

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.

Answer 1

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.