5. An imperfect robot tests motion sensors to see if they are accurate to within

Question

5. An imperfect robot tests motion sensors to see if they are accurate to within the manufacturer's specifications, classifying each motion sensor as accurate or not. It is known that 10% of motion sensors are accurate. If the motion sensor is accurate, there is a 95% chance that the robot classifies the sensor as accurate. If the motion sensor is not accurate, there is a 80% chance that the robot classifies the sensor as not accurate. If the robot classifies a sensor as not accurate, what is the probability that the motion sensor is in fact not accurate?

Explanation / Answer

P(accurate)=0.1 thus P(not accurate)=1-0.1=0.9

P(classified accurate |accurate)=0.95 thus, P(classified not accurate |accurate)=1-0.95=0.05

P(classified not accurate | not accurate)=0.80

Using Baye's rule

P(not accurate | classified as not accurate)=P(classified not accurate | not accurate)*P(not accurate)/P(classified not accurate)

P(classified not accurate)=P(classified not accurate | not accurate)*P(not accurate)+ P(classified not accurate |accurate)*P(accurate) =0.80*0.9+0.05*0.1 =0.725

thus, P(not accurate | classified as not accurate)=0.80*0.9/0.725 =0.99310

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