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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?


0.005

0.015

0.245

0.735

Verified Answer :

erinball

0.245 because of him having the 75% chance of getting it and the test only being 98%

Answer:

Option 3 is correct.

Step-by-step explanation:

Given that 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.

we have to find  the probability that Nathan is not allergic to penicillin and the test predicts it.

As, Nathan has a 75% chance of having the same allergy.

Hence, (100-75)%=25% chance of not having the same allergy.

Also the test predicts given

∴ Probability that Nathan is not allergic to penicillin and the test predicts it is = \(25\%\times 98\%\)

  =\(0.25\times 0.98=0.245\)

Hence, Option 3 is correct.

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