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

Answer 1

im late but if anyone sees this question its 0.9423

Explanation:

The test predicting that he does not have the drug and is correct is 0.98 x 0.25.

Predicting that he does not have the drug but is wrong is 0.02 x 0.75

`( (0.98 * 0.25))/( (0.98 * 0.25) + (0.02 * 0.75) \\\\=( (0.245))/( (0.245) + (0.015)) \\\\= ( 0.245)/( 0.26) \\\\=0.9423`

Got a 5/5 on plato. The other similar answer is 0.245 for the shorter question