a police field drug test kit is used to detect the presence of illegal narcotics

Question

a police field drug test kit is used to detect the presence of illegal narcotics in the blood stream during routine traffic stops. from long term data it is known that approximately 5% of those stopped are under the influence of an illegal narcotic. furthermore, among those that are on narcotics, approximately 95% test positive for illegal drug use. among those who are not on illegal narcotics, approximately 2% test positive for drug use. find the probability that a random person given the test and is on drugs also tests positive for them?

Explanation / Answer

Pr(Any random person who is stopped is under the influence of an illeagal narcotic) = 0.05

Here, Pr(Tested positive l Narcotics user) = 0.95

Pr(Tested positive l not narcho user) = 0.02

Pr(Tested positive when on dugs) = Pr(Tested positive l narcotics user) * Pr(Narco user) / [Pr(Tested positive l narcotics user) * Pr(narco user) + Pr(Tested positive l not narcho user) * Pr(Not narco user)]

= 0.95 * 0.05/ [0.95 * 0.05 + 0.02 * 0.95]

= 0.0475/ 0.0665

= 0.7143

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