Question

A quiz has 4 multiple-choice questions with 4 possible answer choices each. For each question, there is only 1 correct answer.

A student guesses each answer at random. What is the probability of getting exactly 3 questions correct, to the nearest percent?

(3 correct and 1 incorrect)

Answer 1

5%

Explanation:

so, for 3 questions he has a 1 in 4 chances to get it right.

4³ chances, so a 1/4³ probability.

and he has one other question with a 3 in 4 chance to get it wrong.

a 3/4 probability.

that is in total

1/4³ × 3/4 = 3/4⁴

and now we have 4 over 3 combinations as possibilities to get 3 right and 1 wrong.

that is 4! / (3! × (4-3)!) = 4

so our total probability is

4 × 3/4⁴ = 3/4³ = 3/64 ≈ 0.05 = 5%

in other words, the expected quote for him to achieve that result is in 5 out of 100 (or 1 out of 20) attempts.