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: Probability that Nathan is not allergic to penicillin and the test predicts it is 24.5%.

Step-by-step explanation:

Since we have given that

Probability that Nathan having the same allergy that his father and paternal grandfather are prone to =75%

Probability that the test is accurate = 98%

We need to find that Nathan is not allergic to penicillin and the test predicts it.

So, probability that Nathan is not allergic = 100-75=25%

So, we will use "P(A∩B)=P(A)×P(B)"

here, A be the event that Nathan is not having allergy and B be the event that the test predicts it.

We are using the above formula because event A and B are independent events.

so, it becomes,

$P(A\cap B)=P(A)\times P(B)\\\\P(A\cap B)=0.25\times 0.98\\\\P(A\cap B)=0.245\times 100\\\\P(A\cap B)=24.5\%$

Hence,  probability that Nathan is not allergic to penicillin and the test predicts it is 24.5%.

Answer 2

The probability that Nathan is not allergic to penicillin is 1 - 0.75 = 0.25.
The probability that Nathan is not allergic to penicillin and the test predicts it is given by:
$0.25\times0.98=0.245$