The third shiny penny

MediumProbability Combinatorics~5m

A box holds $3$ shiny and $4$ dull pennies. Pennies are drawn one at a time without replacement. What is the probability that it takes more than $4$ draws to remove the third (last) shiny penny?

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More than $4$ draws $\iff$ the first $4$ draws do NOT contain all $3$ shiny pennies.
Compute $\mathbb{P}(\text{3 shiny in first 4})=\binom33\binom41/\binom74$ and subtract from $1$ .

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0.8857 (± 0.001)

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The third shiny penny

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