Probability of an exam, what do you do? Suppose you have an exam that consists of 10 questions, each having two options to choose from. Every correctly answered question gives you 1 point, every unanswered question gives you 0 points, and every wrongly answered question gives you -0.5 points. If you want to maximise your score and you do not know how to answer two out of the ten question, what do you do? What if you only didn't know one? What if each question had three options and you didn't know how to answer one out of the ten questions?

We can just consider maximizing the score on the two question out of the ten. If I don't answer, I'll get 0 points. If I answer randomly you can say I'll get 1 point from one and -0.5 from the other; so I'll get 0.5 So I should try answering.
You can repeat the same argument if you just have a question to answer.
If there are three option, if I don't answer I'll get 0; if I answer I'll get $1*1/3+2/3*(-0.5)=0 $. So the options are quite the same.
