Question

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 wether 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 thecdrug

Answer 1

Nathan has 25% chance of not having the allergy . The test is 98% accurate .
so , 0.25 x 0.98 = 0.2450 . 
 so the answer is 0.245

Answer 2

Answer


Explanation
The probability of Nathan to have the disease is 75% therefore the probality of not having the disease is 25%
The probality of the test detecting that he is not having the disease is 98% therefore the probability of not detecting the disease is 2%
Using a tree diagram there are two outcomes that Nathan will not have the disease
which are:
(75/100X98/100)+(25/100X98/100)=49/50 or 98%