An exam`s points dilemma

Question

On July 2 I have an exam, in this exam will be 40 questions in test with 5 variants of answer for each question.

• For each correct answer will be given +1 point.
• For each incorrect answer will be given -0.25 point
• For each blank answer no points will be given.

I have 40 question at all. Firtly I will be given 20 question for first subject then 10 for second subject and last 10 question for another subject. I know first and last subject for 100% but I don't know the second subject at all.

I want know in percentages, what will be the best at second part of exam, have I answer at random or leave all questions with no answer or answer to part of qustions.

Answer 1

Is this a real world problem or not?

Consideration 1: You probably need 24 points to pass . If you know part 1 and 3 completely, you get 30 points. If you guess all answers wrong, in part 2, you get 2.5 points subtraction. You still have 27.5 points left. But what if you make a small mistake in one if the other parts? You can always make a stupid mistake, bringing you very close to the 24 points you need to pass.

Consideration 2: The expected value of guessing is $\frac{1}{5} \times 1 - \frac{4}{5} \times 0.25 = 0$. The expected value of not guessing is also 0. So it doesn't matter.

Answer 2

For those ten questions, were you to guess completely randomly, you would expect to get $10 \cdot \frac{1}{5} = 2$ questions right and $8$ questions wrong, for a total of $0$ points.

Were you to leave them all blank, you would also get $0$ points. This is probably by-design, so no one thinks they will be better off one way or another. Really your choice just comes down to your level of risk-aversion, and whether you want to take a gamble on beating the odds and answering more than $2$ questions right.

By the way this isn't relevant to the theory of relativity, at all.