Two named cards before a third among four
Question
Four cards, labelled Earth, Air, Fire and Water, are shuffled and turned face up one at a time. You win as soon as both Earth and Air have been revealed, but you lose if Fire is revealed before that happens. What is your probability of winning?
Short answer
. Water is irrelevant. You win exactly when Fire comes last among Earth, Air and Fire, and each of the three is equally likely to be last.
Adapted from Crack, Heard on the Street, Q4.23, p.41; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Counting and Combinatorics
- Sample Spaces, Events, and the Probability Axioms
- Conditional Probability, Total Probability, and Bayes' Rule
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