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Home » Wait—error: $ 16 \cdot 3281 $: - Deep Underground Poetry

Wait—error: $ 16 \cdot 3281 $: - Deep Underground Poetry

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Question: An entomologist is tracking 15 species of pollinating insects in a controlled ecosystem. If she randomly selects 4 species for a detailed genetic analysis, what is the probability that a specific rare species is included in the selection?

📌 To find the probability that a specific species is among the 4 selected, fix one species to be included and choose the remaining 3 from the other 14 species.

📌 Total number of ways to choose 4 species from 15:

📌 Number of favorable outcomes (choosing the specific species and 3 from the other 14):

📌 \binom{14}{3}

📌 So, the probability is:

📌 \frac{\binom{14}{3}}{\binom{15}{4}} = \frac{\frac{14 \cdot 13 \cdot 12}{6}}{\frac{15 \cdot 14 \cdot 13 \cdot 12}{24}} = \frac{364}{1365} = \frac{4}{15}

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