Answer:
(b) 0.00640
Explanation:
Let
P(A|F) = The probability of bags that contain forbidden material trigger an alarm = 0.97 or 97%
P(A| not F)= The probability of bags that do not contain forbidden material also trigger the alarm= 0.15 or 15%
P(F) = the probability that a bag contain forbidden material = 0.001
P(not F) = the probability that a bag does not contain forbidden material = 0.999
Then P(A)= P(F) × P(A|F) + P(not F) × P(A| not F) = 0.001×0.97 + 0.999×0.15 = 0.15082
Then the probability that a bag that triggers the alarm will actually contain forbidden material =
=
≈ 0.0064