A small country has two airports Airport A handles 90 of pas

A small country has two airports. Airport A handles 90% of passengers and Airport B handles 10% of passengers. Security screening at Airport A detects weapons in carry-on luggage 99% of the time. Security screening at Airport B is not as strong, detecting weapons in carry-on luggage 75% of the time. After the screening, a US Air Marshal on an airplane finds a weapon in a passenger\'s carry-on. What is the probability that the passenger passed through Airport A\'s security?

Use Bayes

Solution

Let event A:passengers handeled at airport A P(A)=0.9

B: passengers handeled at airport B P(B)=0.1

P(detecting weapons/A)=0.99

P(detecting weapons/B)=0.75

P(A/weapon not detected)=P(weapon not detected /A)*P(A)/(P(waepon not detected/A)+P(weapon not detected/B)

P(weapon not detected /A)=1-0.99=0.01

P(weapon not detected /B)=1-0.75=0.25

P(A/weapon not detected)=0.01*0.9/0.01*0.9+0.25*0.1=0.2647