A recent test conducted by the Federal Aviation Administration found that guards
ID: 3176614 • Letter: A
Question
A recent test conducted by the Federal Aviation Administration found that guards hired to screen passengers for weapons at the boarding gate had a very poor rate of detection. The detection rates for weapons carried by F.A.A inspectors or placed in their carry-on-luggage averaged 80%, but the rates varied from 34% to 99% for inspectors tested (New York Times. June 18. 1987). Suppose that in a particular city, airport A handles 50% of all airline traffic, while airport B and C handle 30% and 20%, respectively. The detection rates at the three airports are 0.9, 0.5 and 0.4 respectively. If a passenger is carrying a weapon through the boarding gates of one of the airports find The probability that the weapon will be detected. The probability that the weapon will be detected at airport A. The probability that the weapon will be detected at airport B. The probability that the weapon will be detected at airport C.Explanation / Answer
(i)probabilty that weapon will be detected =0.5*0.9+0.3*0.5+0.2*0.4=0.68
(ii)probability that weapon is in A , given detected =0.5*0.9/0.68=0.6618
(iii) =0.3*0.5/0.68=0.2206
(iii)=0.2*0.4/0.68=0.1176