Question

If a part on a production line is present in an inspection area, a sensor detects it with probability 0.99. If a part is not present, the sensor generates a false alarm with probability 0.02. Assume that the probability of a part being present is 0.1.a) What is the probability of seeing a false alarm?b) What is the probability of having a missed detection?

Answer 1

a) P=0.018

b) P=0.001

Explanation:

The probability of a false alarm is equal to the probability of not having a part (0.9) multiplied by the probability of generating a alarm if there is no part (0.02).

`P_(FA)=P_(np)*P_a=(1-0.1)*0.02=0.9*0.02=0.018`

The probability of having a missed detection is equal to the probability of having a part (0.1) multiplied by the probability of not detecting it if it is there (0.01).

`P_(miss)=P_p*P_(nd)=0.1*0.01=0.001`