What is the probability of getting exactly 2 correct answers if you make random guesses ?

Answer 1

We'll assume answering each question is an independent event (that is the answer we choose for question 1 doesn't narrow our options for question 2, or vice versa). We will also assume all questions have the same probability of success when guessing randomly. Let's call the probability of getting any question right by guessing randomly "p", and the total number of questions "n".

The probability of getting exactly 2 questions right would be given by the formula:

P(n) = C(n, 2) * p² * (1-p)^n-2