Answer:
No.
Explanation:
Well, honestly not sure how to solve this but I'll try.
Each correct answer is giving 4 points but the probability to choose the correct one is 1/5
Each incorrect one gives -2 points and the chance to pick a wrong answer is 4/5.
Obviously, the chance to lose points is more. But is taking the risk and guessing worth it? Well, it depends on how many points the correct answer gives. If it makes up for the possible loss of points, then it is in his interest to guess, otherwise he will end up losing more than they win.
If we sum the two chances to find averagely how many points the student will get, then I guess that would be the correct answer:
4(1/5) + (-2)(4/5) = 4/5 - 8/5 = -4/5
He will get averagely -4/5 points, so I believe it isn't in his interest. It means that the points he gets don't make up for the possible loss of points if you choose answers randomly. (Wow, I'm glad teachers don't do this on tests 0_0)
This is my theory though, not sure how to go for solving this, just thinked logically. I hope this helps, but don't trust me and copy paste my answer on your test or whatever. Think if this is correct first because I'm not sure