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. what is the probability that nathan is not allergic to penicillin and the test predicts it?

The probability is 0.245

Step-by-step explanation:

Call B the event: Nathan is allergic to penicillin.

We know from your family history that

So the probability that Nathan is not allergic to penicillin is

Then, the test has 98% accuracy, that is: The probability that the test result is correct is 0.98.

So the probability that the test predicts that Nathan is not allergic and is not really allergic is:

There is a 24.5% chance that Nathan is not allergic and the test predicts it