Probability using Bayes Theorum Here's a problem which me and a friend had an argument over the answer. Could someone please resolve the dispute People are first subjected to test_1, if the test_1 is positive then person is taken for test_2. Test_2 will reveal whether the person has been under the influence of the drug. The test_1 yields positive results among 95% of drug using people and gives positive results among 8% of non drug users. Stats say 1 out of 25 use the drug. Calculate the probability of a randomly person being unnecessarily subjected to a test_2 after a positive test_1?

(24/25)*8/100 will be the probability of wrong diagnosis and subjected to test 2. And that is what Bayes theorem is , conditional provability.