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. What is the probability that Nathan is not allergic to penicillin and the test predicts it?

Answer 1

Answer:

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

$P(B) = 0.75$

So the probability that Nathan is not allergic to penicillin is

$P(\~B) = 1-P(B) = 0.25$

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:

$P = 0.25 * 0.98 = 0.245$

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