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📅 May 11, 2026 👤 scraface

May 11, 2026

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📌 We want $ P(X = 5) $:

📌 P(X = 5) = \binom{10}{5} (0.3)^5 (0.7)^5

📌 $ \binom{10}{5} = 252 $

📌 $ (0.3)^5 = 0.00243 $

📌 $ (0.7)^5 = 0.16807 $

📌 Now multiply:

📌 P(X = 5) = 252 \cdot 0.00243 \cdot 0.16807 \approx 252 \cdot 0.0004084 = 0.1029

📌 Thus, the probability that it rains on exactly 5 out of 10 randomly selected days is approximately:

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