A drug test is accurate 96% of the time. If the test is given to 1900 people who have not taken drugs, what is the probability that at least 78 will test positive? Probability =

Answer 1

.04 x 1900 = 76

4% probability of a false positive

But that assumes the false positive and false negative rates are the same. Generally, they aren't. With more information, you could use Bayes' Theorem to solve this problem.

Bayes Theorem is P(p/~D)P(~D) = P(~D/p)P(p)

Let P(p/~D) = the probability of testing positive for drugs when no drugs were used = false positive

P(~D) = probability of not using drugs

P(p) = probability of a positive test

P(~D/p) = probability of not using drugs given a positive test result for drugs

P(p/~D) = P(~D/p)P(p)/[(P(~D/p)P(p) + P(~D/~p)P(~p)]

The test can be reliable in two different ways, few false positives or few false negatives. The two errors generally are not the same.