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?

The answer is : The probability that Nathan is allergic to penicillin and the test predicts it is 0.735.

Nathan has an infection and his doctor wanted him to take penicillin. But he has a 75% probability of being allergic to penicillin.

The doctor performs a test which is 98% accurate.

This implies that even if Nathan is allergic, the test is only 98% accurate of identifying the allergy.

Now, we have been asked to find the probability of both these events happening.

Therefore, probability that Nathan has the allergy and test predicts it is

= 75% x 98%

=>

=

Hence, the answer is : The probability that Nathan is allergic to penicillin and the test predicts it is 0.735.

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