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Home » Domino’s Emergency Pizza? Feast Fest Soon—Get Your Favorite Slice, Fast & Fresh! - AMAZONAWS

Domino’s Emergency Pizza? Feast Fest Soon—Get Your Favorite Slice, Fast & Fresh! - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 #### 168.75**Question:** A seismologist is analyzing data from 7 different seismic stations. Each station can independently detect an earthquake with a probability of \( \frac{1}{2} \). What is the probability that exactly 4 out of the 7 stations detect an earthquake?

📌 This is a binomial probability problem where we have \( n = 7 \) trials (seismic stations), each with a probability \( p = \frac{1}{2} \) of detecting an earthquake. We want to find the probability of exactly \( k = 4 \) successes (detections).

📌 The formula for the binomial probability is:

📌 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

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