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📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 $ P(0) = \binom{6}{0} (0.3)^0 (0.7)^6 = 1 \cdot 1 \cdot 0.117649 = 0.117649 $

📌 $ P(1) = \binom{6}{1} (0.3)^1 (0.7)^5 = 6 \cdot 0.3 \cdot 0.16807 = 0.302526 $

📌 $ P(2) = \binom{6}{2} (0.3)^2 (0.7)^4 = 15 \cdot 0.09 \cdot 0.2401 = 0.324135 $

📌 P(X < 3) = 0.117649 + 0.302526 + 0.324135 = 0.74431

📌 \boxed{0.74431}

📌 Question: A mix of 5 AI models and 3 human analysts sit around a circular table. How many distinct seating arrangements are possible if rotations are considered the same?

📌 Solution: For circular arrangements of $ n $ distinguishable people, the number of distinct arrangements is $ (n-1)! $, since rotations are equivalent.

📌 Here, we have $ 5 + 3 = 8 $ distinguishable individuals.

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