Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all

Question

3 months ago

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Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all

ergic 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?
PLEASE HELPPPP! IM TALING A PLATO TEST

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-02-21T12:09:19+03:00

Let the events be defined as follows:
A=Nathan suffers from an allergy
~A=Nathan does not suffer from an allergy
T=Nathan receives a positive test result
~T=Nathan does not receive a positive test result

According to the provided data,
P(A)=0.75 [ probability indicating that Nathan is allergic ]
P(T|A)=0.98 [ probability of obtaining a positive test result if Nathan is allergic to Penicillin]

We aim to calculate the probability that Nathan is both allergic and tests positive
P(T n A)

Using the definition of conditional probability,
P(T|A)=P(T n A)/P(A)
By substituting the known values,
0.98 = P(T n A) / 0.75
We then solve for P(T n A)
P(T n A) = 0.75*0.98 = 0.735

Hope this assists you!!