Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all
ergic to penicillin, Nathan had a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. What is the probability that Nathan is allergic to penicillin and the test predicts it? 0.005
Given that Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan had a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate.
Probability that Nathan is allergic to pennicillin and the test predicts it
=Prob (Nathan is allergic)*P(test predicts it correct)