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📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 \( P(X=5) = \binom{150}{5} (0.03)^5 (0.97)^{145} \).

📌 Approximate with Poisson: \( \lambda = 150 \times 0.03 = 4.5 \).

📌 \( P(X=5) = \frac{e^{-4.5} (4.5)^5}{5!} \).

📌 \( e^{-4.5} \approx 0.011109 \), \( 4.5^5 = 1845.5625 \), \( 5! = 120 \).

📌 \( P = \frac{0.011109 \times 1845.5625}{120} \approx \frac{20.48}{120} \approx 0.1707 \).

📌 More accurately: \( P = \binom{150}{5} (0.03)^5 (0.97)^{145} \).

📌 \( \binom{150}{5} = \frac{150 \cdot 149 \cdot 148 \cdot 147 \cdot 146}{120} = 591,600,276 \)

📌 \( (0.03)^5 = 2.43 \times 10^{-8} \)

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