Probability Worksheets Page 4

PROBABILITY Worksheet #3
Suppose a drug-sniﬃng dog correctly identiﬁes illegal drugs 80% of the time.
This means that:
(1) If a person has illegal drugs on them, 80% of the time the dog will correctly
identify the drugs and start barking, and 20% of the time the dog will miss
the drugs and not bark.
(2) If a person does not have illegal drugs on them, 80% of the time the dog
will correctly not bark, but 20% of the time the dog will incorrectly start
barking.
Suppose that you are a police oﬃcer with such a dog working a Jay-Z concert.
At the Jay-Z concert, 1 in every 100 people has illegal drugs on them. If your
K-9 partner starts barking at a person, what is the probability that that person
actually has illegal drugs?
are sniﬀed by the dog, and ﬁll out the following table.
# of correct negatives
# of false positives
# of people without drugs
(people without drugs,
(people without drugs,
and dog does not bark)
and dog does bark)
# of correct positives
# of false negatives
# of people with drugs
(people with drugs,
(people with drugs,
and dog does bark)
and dog does not bark)
P(person that the dog barks at has drugs) =
Question: In light of this probability, how do you think you should treat suspects
that the dog barks at before you search them and actually determine whether
or not they are in possession of illegal drugs?