Question

Select the correct answer.
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan had 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 allergic to penicillin and the test predicts it?

Answer 1

Answer:

$P=0.735$

Step-by-step explanation:

Call A to the event in which Nathan is allergic to penicillin

So

$P (A) = 0.75$

$P (A') = 1-P (A) = 0.25$

Call B the event in which the skin test predicts correctly.

So:

$P (B) = 0.98\\P (B ') = 1-P (B) = 0.02$

We look for the probability that Nathan is allergic to penicillin and the test predicts it.

This is $P (A\ and\ B)$.

$P (A\ and\ B) = P (A)*P (B)\\\\P (A\ and\ B) = 0.75 * 0.98\\\\P (A\ and\ B) = 0.735$