Yesterday, I participated in a UKMT Math Challenge, and came up with this question:
each question in the UKMT is multiple choice, with 5 options.
For the first 15 questions, you get 5 marks for the correct answer. You don't lose marks for incorrect answers.
For the next 5 questions (Q16-20) you lose a mark for each wrong answer, but earn 6 marks for each correct one.
For the following 5 questions (Q21-25) you lose 2 marks for each wrong answer, and earn 6 marks for each correct answer.
What is the expected amount of marks I will get if I just randomly guess everything?
This problem is roughly of the level of difficulty of the Intermediate UKMT Math Challenge.This problem is part of this set.