You are to participate in an exam for which you had no chanc

You are to participate in an exam for which you had no chance to study, and for that reason cannot do anything but guess for each question (all questions being of the multiple choice type, so the chance of guessing the correct answer for each question is 1/d, d being the number of options (distractors) per question; 220 so in case of a 4-choice question, your guess chance is 0.25). Your instructor offers you the opportunity to choose amongst the following exam formats: I. 6 questions of the 4-choice type; you pass when 5 or more answers are correct; II. 5 questions of the 5-choice type; you pass when 4 or more answers are correct; III. 4 questions of the 10-choice type; you pass when 3 or more answers are correct. Rank the three exam formats according to their attractiveness. It should be clear that the format with the highest probability to pass is the most attractive format. Which would you choose and why?

Solution

6 questions of the 4-choice type; you pass when 5 or more answers are correct in this we have 4 options so the probability of gettinf the right answer is 1/4 = 0.25, also we have to answer 5 correct.

5 questions of the 5-choice type; you pass when 4 or more answers are correct in this we hace 5 options so the probability of gettinf the right answer is 1/5 = 0.20 and we have to get 4 right out of 5

4 questions of the 10-choice type; you pass when 3 or more answers are correct in this the probability of getting the right answer is 1/10 =0.10 and we have to get the 3 answer right in this,

as we have seen that the probability is decreasing of getiing right answers as we are having more options so the format which have the highest probability of getting the right answer will be ranked 1st and so on

rank 1 = format 1

rank 2 = format 2

rank 3 = format 3