Knew the answer given it was marked correct

Question

On a multiple-choice test where every question has $5$ options, a student either knows the correct answer (and then picks it) or guesses uniformly at random. For any question the student knows the answer with probability $0.6$ . If a particular answer turned out correct, what is the probability the student actually knew it?

Short answer

$15/17$ . By Bayes' rule, $\mathbb{P}[\text{knew}\mid\text{correct}]=\dfrac{0.6}{0.6+0.4\cdot0.2}=\dfrac{0.6}{0.68}=\dfrac{15}{17}$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Conditional Probability, Total Probability, and Bayes' Rule
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating
Sample Spaces, Events, and the Probability Axioms

Start with a free lesson: Probability Fundamentals is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free