Answer
If there is no deduction, the student, of course, will try to guess the correct answer: the expected value is positive. But, if there is a penalty for wrong answers, the expected value is 0. If he tries to guess many questions, it is expected that he will make no point.
Work Step by Step
If there is no deduction for wrong answers:
Suppose b is the correct answer. So, if the student chooses b, he receives 1 point. For any other option, 0 points.
$E(X)=μ_X=Σ[x.P(X)]=0\times\frac{1}{5}+1\times\frac{1}{5}+0\times\frac{1}{5}+0\times\frac{1}{5}+0\times\frac{1}{5}=\frac{1}{5}$
