The Fundamental Counting Principle

Question

When a multiple choice question has 5 choices, the probability of getting question right by randomly guessing is 1/5. What is the probability you would get a question wrong by guessing? What is the probability you would get all 10 questions wrong by guessing? Explain.

Answer 1

There are two outcomes to a multiple choice question: either you get it right, or you get it wrong.

Let p = probability you get the question right.

Let q = probability you get the question wrong.

Since these are the only two outcomes, p+q = 1.

Since p = 1/5, q must be 4/5.

The probability of two independent events happening is just the product of their individual probabilities.

So, the probability of getting all 10 questions wrong is just:

q*q*q*q*q*q*q*q*q*q = (4/5)^10 = 0.10737

You have about a 10% chance of getting them all wrong.