Question

A new test for a rare genetic condition has a false positive rate of 0.29% and a false negative rate of 0.87%. Assume that 99.42% of all tested individuals do not have the rare genetic condition. What is the probability that someone who tests positive actually does have the rare genetic condition?

Answer 1

P(don't have the rare genetic condition) = 0.9942

P(tests positive | don't have the rare genetic condition) = 0.0029

P(tests negative | have the rare genetic condition) = 0.0087

P(tests positive | have the rare genetic condition) = 1 - P(tests negative | have the rare genetic condition) = 1 - 0.0087 = 0.9913

P(tests positive) = P(tests positive | don't have the rare genetic condition) * P(don't have the rare genetic condition) + P(tests positive | have the rare genetic condition) * P(have the rare genetic condition)

                          = 0.0029 * 0.9942 + 0.9913 * (1 - 0.9942)

                          = 0.00863272

P(have the rare genetic condition | tests positive) = P(tests positive | have the rare genetic condition) * P(have the rare genetic condition) / P(tests positive)

                                                                              = 0.9913 * (1 - 0.9942) / 0.00863272

                                                                              = 0.666