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Question

Suppose that, in a particular city, airport A handles 50% of all airline traffic, and airports B and C handle 30% and 20%, respectively. The detection rates for weapons at the three airports are .9, .8, and .85, respectively. If a passenger at one of the airports is found to be carrying a weapon through the boarding gate, what is the probability that the passenger is using airport A? Airport C?

Solution

VerifiedStep 1

1 of 4Let $E_A, E_B$ and $E_C$ be the event that airport $A, B$ and $C$ is used by passenger, respectively.

Let $D$ be the event that weapon is detected.

Given:

$P(E_A)=.5~~~~~P(E_B)= .3~~~~~ P(E_C)= .2$

$P(D| E_A)=0.9 ~~~~P(D| E_B)= .8 ~~~~P(D| E_C)= 0.85$

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