UKMT Math Challenge
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 .
The answer is 15.
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1 solution
The probabillity of solving any given question is 1/5, so we expect that one question is solved in every 5 questions. In the first group of 15 questions we expect to solve 3 questions: that's 15 points. In the next 5 questions, we expect to answer one correctly, for 6 points, and lose 4 marks on the other 4 questions: that's a total of 2 marks gained there. The last 5 questions: we expect to get 6 points for one correct, and lose 8 marks for 4 wrong: that's -2 marks. The 2 and -2 from the last 10 questions cancel out, leaving us with 15 marks.