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

The answer is 0.2450

To calculate this, a multiplication rule is used. The multiplication rule calculates the probability that both of two events will occur. In this method, the probabilities of each event are multiplied.

In this situation, we have two events occurring simultaneously:

1. Nathan is not allergic to penicillin. The probability that Nathan is not allergic to penicillin is:

1 - the probability of having the allergy.

If the probability of having the allergy is 75% = 0.75, then the probability that Nathan is not allergic to penicillin is:

1 - 0.75 = 0.25

2. The probability that the test is accurate: 98% = 0.98

By using the multiplication rule:

0.25 × 0.98 = 0.245

Therefore, the probability after the test that Nathan is not allergic to the drug is 0.245 = 24.5%.