Question

All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material?

Answer 1

0.00643

Explanation:

The probability of a bag triggering the alarm is given by the probability of the bag containing forbidden material and triggering the alarm plus the probability of the bag NOT containing forbidden material and triggering the alarm:

`P(T) = (1)/(1,000)*0.97 + (999)/(1,000)*0.15\\P(T) = 0.15082`

The probability that a bag that has triggered the alarm contains forbidden material is:

`P(F)=((1)/(1,000)*0.97)/(P(T)) =((1)/(1,000)*0.97)/(0.15082)\\P(F)=0.00643`