A test with 100 MCQ were set and each question have 4 choices. One mark will be allocated for each correct answer.

Question

1. If you know the answer for 40 questions and guess the answer randomly for other questions, how many marks will you expect to get?
2. To discourage students from simply guessing the answer randomly, teachers decided to give 2 marks for each correct answer and deduct 1 mark for all wrong answer, how many marks will you expect to get if you guess the answer randomly for all the question. 

Answer 1

1.  You get 40 correct, for 40 points.  That leaves 60 questions to guess on.  Since there are 4 choices for each question, the probability of getting the right answer on each one is 1/4.  So that means that your expected number of correct guesses is 1/4 * 60 = 15.  Add that to the 40 points for your other correct answers, and you get 55.

 

2. If you guess randomly for ALL the questions (which is the way the question was stated), you're going to come out with a pretty bad score.

 

The expected number of right answers is 1/4 * 100 = 25.  At 2 points each, that's 50 points

 

But the expected number of wrong answers is 3/4 * 100 = 75.  With 1 point deducted for each, that's 50 points for the correct answer minus 75 for the wrong answers, which is a negative score of -25.