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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?

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  • $\begingroup$ $\frac{24}{25}\cdot\frac{8}{100}$. No need to apply Bayes here. $\endgroup$ Commented Nov 9, 2016 at 12:49
  • $\begingroup$ So you are looking for the probability of a false positive, which is P(test_1 positive|not a drug user) $\endgroup$ Commented Nov 9, 2016 at 12:49
  • $\begingroup$ Bram28 Yes, the probability of a false positive $\endgroup$ Commented Nov 9, 2016 at 12:56
  • $\begingroup$ barak manos - I got to your answer after using the Bayes theorem, so I just wanted to know when should we apply and when not apply Bayes. How do you come to the conclusion. $\endgroup$ Commented Nov 9, 2016 at 13:10

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(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.

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