Radar Detection: False Alarms & Misses

Problem 2.5 • Given an alarm sounds, what's the probability of an actual plane?

📡 Radar Simulation

📊 Confusion Matrix

Alarm
No Alarm
Plane ✈️
True Positive
—
Miss
—
No Plane
False Alarm
—
True Negative
—
Sensitivity (TPR)
0.99
False Alarm Rate (FPR)
0.10
Specificity (TNR)
0.90
Miss Rate (FNR)
0.01

⚙️ Parameters

P(Plane) - Prior probability 0.05
P(Alarm|Plane) - Detection rate 0.99
P(Alarm|No Plane) - False alarm rate 0.10

📐 Bayes' Calculation

P(Plane|Alarm) =
P(Alarm|Plane) × P(Plane)
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P(Alarm)
P(Alarm) = 0.145
(Total Probability)
P(Plane | Alarm)
0.342

Even with a 99% detection rate, only 34.2% of alarms are real planes!