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Home » 3rd term: \(15 \times 3 = 45\) - Nelissen Grade advocaten

3rd term: \(15 \times 3 = 45\) - Nelissen Grade advocaten

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 A robotics engineer programs a swarm of 10 autonomous inspection robots. Each robot independently detects a flaw with probability 0.8. What is the probability that at least 8 robots detect a flaw during a single inspection cycle?

📌 This is a binomial probability: n = 10, p = 0.8, find P(X ≥ 8) = P(X=8) + P(X=9) + P(X=10).

📌 P(X=k) = C(10,k) (0.8)^k (0.2)^(10−k)

📌 P(X=8) = C(10,8) (0.8)^8 (0.2)^2 = 45 × 0.16777216 × 0.04 ≈ 0.30199

📌 P(X=9) = C(10,9) (0.8)^9 (0.2)^1 = 10 × 0.134217728 × 0.2 ≈ 0.268435

📌 P(X=10) = C(10,10) (0.8)^10 = 1 × 0.1073741824 ≈ 0.10737

📌 Sum ≈ 0.30199 + 0.268435 + 0.10737 = <<0.30199+0.268435+0.10737=0.677795>>0.6778 (rounded to 4 decimal places)

📌 #### 0.6778

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