Assume a test in multiple-choice format taken by a student with no prior knowledge of the test subject and he is going to pick answers in a random way.
- What is the probability of him getting 100% in the test?
- What is the average probability of him getting atleast 40% in the test?
- Given N number of students take the test(assuming all pick answers at random), what is the average score?
- What effect do the variables number of questions, students and number of choices have in the overall average percentage of marks?
- Do the results considerably vary across tests?
- What would be a better strategy to get more marks - to pick answers at random or to select a single choice (such as A)
Assuming Q be the number of questions and Q, C be the number of choices and N the number of students and for this illustration let Q be 10, C be 3 and N be 1000, I arrived at the following
1/(C^Q). So 1/(3^10)
The probability of getting at least 40% is 1 minus probability of getting less than 4 questions correct. So 1-(1/(3^1+3^2+3^3))
1/C. I run a simulation program and got the results but can't mathematically prove or deduce it.
Deducing from 3 above, only C is going to have an impact on the average score irrespective of Q and N (assuming N to be greater)
Since only C is the major determinant of overall scores, the results aren't going to vary across tests
Randomly picking answers is better than picking a same choice. Again I ran a simulation and deduced it but cannot mathematically deduce it.
Am I right? How to mathematically deduce the answer for Question 3 and Question 6