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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 \( P(A) = 0.8 \), \( P(B) = 0.7 \), \( P(C) = 0.6 \)

📌 \( P(A \cap B \cap C) = 0.3 \)

📌 Exactly two detections = \( [P(A \cap B) + P(B \cap C) + P(A \cap C)] - 3 \times P(A \cap B \cap C) \)

📌 Assuming independence:

📌 \( P(A \cap B) = 0.8 \times 0.7 = 0.56 \), \( P(B \cap C) = 0.7 \times 0.6 = 0.42 \), \( P(A \cap C) = 0.8 \times 0.6 = 0.48 \)

📌 Sum: \( 0.56 + 0.42 + 0.48 = 1.46 \)

📌 Subtract overcount: \( 1.46 - 3 \times 0.3 = 1.46 - 0.9 = 0.56 \)

📌 So 56% detect exactly two.

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