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?

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,

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

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x