Question

. Suppose 2% of people have Syndrome X. We have a Syndrome X detecting test which gives which gives a positive result for 90% of people who do have the syndrome, but also gives a positive result for 10% of people who don’t actually have the syndrome. A patient comes in and gets a positive result. What are the chances they have Syndrome X? For full credit, you must show your work.

Answer 1

P(people have Syndrome X) = 0.02

P(positive result | have Syndrome X) = 0.9

P(positive result | don't have Syndrome X) = 0.1

P(positive result) = P(positive result | have Syndrome X) * P(have Syndrome X) + P(positive result | don't have Syndrome X) * P(don't have Syndrome X)

                           = 0.9 * 0.02 + 0.1 * (1 - 0.02)

                           = 0.116

P(have Syndrome X | positive result) = P(positive result | have Syndrome X) * P(have Syndrome X) / P(positive result)

                                                           = 0.9 * 0.02 / 0.116

                                                           = 0.1552 ( ans)