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📅 May 4, 2026 👤 scraface

May 04, 2026

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Since X = sum of expected values over 3 selected communities:
E[X] = 3 × 3 = <<3*3=9>>9.
A robotics engineer programs a swarm of 10 autonomous inspection robot...
This is a binomial probability: n = 10, p = 0.8, find P(X ≥ 8) = P(X=8...
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=0.6777...
#### 0.6778

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