Question

The Transportation Security Agency (TSA) uses drug-sniffing dogs. A new breed will be checked for efficiency. Let D be the event that a piece of luggage contains drugs, B the event that a dog barks in the presence of a piece of luggage. What probability is the TSA interested in determining?
A. P(B|D) (i.e., the probability of B given D)
B. P(D|B) (i.e., the probability of D given B)

C. P(D and B)
D. P(B)

Answer 1

We are given the events definitions here as:

• D is the event that a piece of luggage contains drugs
• B is the event that a dog barks in the presence of a piece of luggage

The test efficiency is defined as the percentage of total tests where we get the correct prediction - that is true positives and true negatives.

The probability of true positive is computed here as:
P(B | D) that is the probability that the dog barks on a luggage when it contain the drugs.

Therefore P(B | D) is the required probability that we are interested in here.