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

February 22, 2026

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

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A volcanologist monitors three seismic sensors near a volcano. Sensor A detects activity 80% of the time, Sensor B 70%, and Sensor C 60%. All three detect simultaneously in 30% of active periods. Assuming independence for estimation, what percentage of active periods do exactly two sensors detect the activity?
Let total active period be 1000 units.
\( P(A \cap B \cap C) = 0.3 \)
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:

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