No face cards before the two of hearts

Question

A shuffled $52$ -card deck is dealt face up until the two of hearts turns up. What is the probability that no jack, queen or king has appeared before it?

Short answer

$\tfrac1{13}$ . Only the relative order of the two of hearts and the $12$ face cards matters. Each of these $13$ cards is equally likely to come first, so the two of hearts leads with probability $\tfrac1{13}$ .

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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