Toasted pancake flipped over

Question

Three pancakes lie on a plate: one browned on both faces, one browned on a single face, and one browned on neither. You take a pancake at random, it lands with a random face up, and the face you see is browned. What is the probability that the underside is browned too?

Short answer

$\tfrac23$ . Each of the six faces is equally likely to be the one on top. Three faces are browned, and two of those belong to the doubly browned pancake, so the conditional probability is $\tfrac23$ , not $\tfrac12$ .

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

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Lessons behind this question

Conditional Probability, Total Probability, and Bayes' Rule
Counting and Combinatorics
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating

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