No face card before the two of hearts

MediumProbability Combinatorics~4m

A standard $52$ -card deck is shuffled and dealt one card at a time until the $2\heartsuit$ appears. What is the probability that no King, Queen, or Jack appears before the $2\heartsuit$ ?

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Only the $2\heartsuit$ and the $12$ face cards matter; ignore the other $39$ .
"No face before it" = the $2\heartsuit$ is first of those $13$ : probability $1/13$ .

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0.0769 (± 0.001)

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Asked at: Jane Street, SIG

No face card before the two of hearts

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