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Home » \[ s^2 = 2^2 = 4 \] - AMAZONAWS

\[ s^2 = 2^2 = 4 \] - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Question: A researcher analyzing gene expression in 12 modified rice plants finds that 9 show enhanced drought resistance. If 4 plants are randomly selected for detailed genomic sequencing, what is the probability that at least 3 of them have enhanced resistance?

📌 Solution: We compute the probability of exactly 3 or exactly 4 successful selections (enhanced resistance).

📌 Total ways to choose 4 plants: $inom{12}{4} = 495$.

📌 Favorable cases:

📌 Exactly 3 enhanced, 1 not: $inom{9}{3} \cdot inom{3}{1} = 84 \cdot 3 = 252$.

📌 Exactly 4 enhanced: $inom{9}{4} = 126$.

📌 Total favorable: $252 + 126 = 378$.

📌 Probability: $rac{378}{495} = rac{126}{165} = rac{42}{55}$.

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