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s = \frac363 = 12 \text cm - AdVision eCommerce

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

📌 Substitute \( n = 7 \), \( k = 4 \), and \( p = \frac{1}{2} \):

📌 P(X = 4) = \binom{7}{4} \left( \frac{1}{2} \right)^4 \left( \frac{1}{2} \right)^{3}

📌 Calculate \( \binom{7}{4} \):

📌 \binom{7}{4} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35

📌 So, the probability becomes:

📌 P(X = 4) = 35 \times \left( \frac{1}{2} \right)^7 = 35 \times \frac{1}{128} = \frac{35}{128}

📌 Thus, the probability that exactly 4 stations detect an earthquake is \(\boxed{\frac{35}{128}}\).

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