Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan has 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. If the test predicts that Nathan is not allergic to penicillin, what is the probability after the test that Nathan is not allergic to the drug?

A. 0.1135

B. 0.2450

C. 0.9423

D. 0.9932

Question

Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan has 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. If the test predicts that Nathan is not allergic to penicillin, what is the probability after the test that Nathan is not allergic to the drug?

A. 0.1135

B. 0.2450

C. 0.9423

D. 0.9932

anonymous · Answer

@timo86m

anonymous · Answer

you know how to do this? @Koikkara

koikkara · Answer

@sugahead12 Nathan has 
 0.75 chance of allergy
 0.25 chance of no allergy

test is
 0.98 correct
 0.02 incorrect

Nathan is not allergic to penicillin and the test predicts it
or in other words

Nathan no allergy and test incorrect
multiply the probabilities:  Pr(no allergy) * Pr(incorrect) = 0.25*0.02 = 0.005

anonymous · Answer

Yeah i get that but how do i get the real answer after multiplying that

koikkara · Answer

@sugahead12 Seems like it's been answered daily, have a look at closed questions too !

Nice to meet You !! Have A Good Day !!

anonymous · Answer

Hey if you still want the answer it's C; 0.9423