A statistics teacher decides to give his students a 5-question multiple-choice quiz with 4 possible answers for each question. If a student decides to randomly guess on each question, what is the probability the student will get 2 questions correct?

Let’s start with all possible answers which is equal to 5^6=3125 .

First of all, i ll change the question to :

“How many different way to answer the quiz with only 2 permitted

Now we can organize our job in tow tasks:

N° 1 : how the 2 mistakes can be distributed ? the answer is (2 c 6) = 15.

N°2 : how many ways those mistakes can be shown ? the answer is 4^ 2 = 16.

The answer is 16*15/5^6 = 7.68 %