Turning up air and water before fire

Question

Four face-down cards are labelled earth, air, fire and water, in a random order. You turn them over one by one. You win if both the air card and the water card are revealed before the fire card. What is your probability of winning?

Short answer

$\tfrac13$ . The earth card is irrelevant. Among air, water and fire, all $3!$ relative orders are equally likely, and you win exactly when fire comes last, which has probability $\tfrac13$ .

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

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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