Question

Airport security screens baggage for a certain substance using both a detection apparatus and a trained dog. Experience has shown that if the substance is present, the apparatus will detect it with probability .82 and the dog will detect it with probability .69. Assume that the functioning of the apparatus is independent of the behavior of the dog (so that, for example, if the substance is present, the dog detects it with probability .69 independent of whether or not the apparatus detects it), and assume that the substance is present in a piece of baggage. What is the probability that it will be detected by both the apparatus and the dog? What is the probability that it will be detected by at least one of the apparatus and the dog? If we now also assume that the dog is only used to screen baggage which has been “passed” by the apparatus, what is the probability that bag in which the substance is present is detected by the dog?

Answer 1

1) probability that it will be detected by both the apparatus and the dog =0.82*0.69=0.5658

2) probability that it will be detected by at least one of the apparatus and the dog

=1-P(none detect it)=1-(1-0.82)*(1-0.69)=0.9442

3) probability that bag in which the substance is present is detected by the dog

=P( apparatus not detect and dog detects it)=(1-0.82)*0.69=0.1242