Percent Error of a Typical Exam

Question

In the Japanese national mathematics exam system, students are asked to work questions and bubble in the last digit of the answer. Thus the "scantron" form has ten possible answers for each question: 0, 1, ..., 9. If scoring correction is not used, what is the percentage error of a typical exam where the test-taker achieves $k$ correct answers on an $n$ question exam?

It is easy to see that the probability of answering each question correctly is 0.1 (assuming a random guess). However, I have no clue how to use that information to go about answering the question.

Answer 1

This may be too simplistic, but the other approach I could think of looked way too hard, so:

Assume the student knows $t$ right answers, and the other $n-t$ answers are complete guesses. We would then expect the student to get $t+0.1(n-t)$ points on the test. Set that equal to $k$ and solve for $t$ in terms of $k$. You can then find the difference $t-k$ and divide by $k$ (that seems like the most likely if we want to find the percent error in the observed measurement).

Answer 2

I am thinking we might be in the same course. I e-mailed the professor about this same issue earlier in the week. He responded by saying, "If you have two measurements S and T, the percent error can be (S-T)/S or (T-S)/T, where the denominator is generally considered the basic (sometimes first) measurement". I hope this helps.