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. if the test predicts that nathan is not allergic to penicillin, what is the probability after the test that nathan is not allergic to the drug?

a.)0.1135 b.)0.2450 c.)0.9423 d.)9932

Option b.) 0.245 would be correct.

Step-by-step explanation:

There is given two probabilities events  occurring simultaneously

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% = 0.25 chance of not having the same allergy

The probability that the test is accurate: 98% = 0.98.

By using the multiplication rule -

25% × 98% = 0.25 × 0.98 = 0.245

Therefore the probability after the test that Nathan is not allergic to the drug would be 24.5% or 0.245.