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 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

0.735

Explanation:

Let A be the event of being allergic to penicillin and T be the event that the test predicted the allergy is accurate.

According to the question,

There is 75% chance of having the allergy.

⇒ Probability of being allergic to penicillin, P(A) = 75 % = 0.75,

Also, the test is 98% accurate.

⇒ Probability that the allergy is predicted by the test, P(B) = 98% = 0.98

Since, both A and T are independent events,

Thus, the probability that Nathan is allergic to penicillin and the test predicts it

= P(A) × P(T)

= 0.75 × 0.98

= 0.735

Answer 2

There is a 73.5% chance that Nathan is allergic to penicillin and the test predicts it.

75% * 98% = 73.5%

.75 * .98 = .735