25 You are to participate in an exam for Which YOU had no ch

25. 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 lid, d being the number of options (dis-tractors) per question; 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. questions of the 5-choice type; you pass when 4 or more answers are correct; lii. 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

1st format :

Number of questions : 6
Choices : 4
Pass : 5 or more are correct

P(pass) = P(5 correct) + P(all 6 correct)
= (6C5)*(0.25)^5*(0.75)^1 + (0.25)^6
= 0.004638671875

2nd format :

Number of questions : 5
Choices : 5
Pass : 4 or more are correct

P(pass) = P(4 correct) + P(all 5 correct)
= (5C4)*(0.2)^4(0.8)^1 + (0.2)^5
= 0.00672

3rd format :

Number of questions : 4
Choices : 10
Pass : 3 or more are correct

P(pass) = P(3 correct) + P(all 4 correct)
= (4C3)*(0.1)^3*(0.9)^1 + (0.1)^4
= 0.0037

So, as can be seen, 2nd format > 1st format > 3rd format

So, in order of most attractive to least attractive : 2nd , 1st , 3rd

Since the second has the highest probability, the 2nd format is the most attractive.....