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 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

Answer 1

It's not A. So, how do I complete this @Hero ?

Answer 2

Make a tree:

Let P(a) represent the probability Nathan is allergic to Penicillin
and P(b) represent the probability Nathan is not allergic to Penicillin
and P(c) represent the probability that the test gives a correct result.
and P(d) represent the probability the test does give a correct result.

Answer 3

Oh wait, there's more possible results. Hang on.

Answer 4

It's C. Isn't it?

Answer 5

Let me add one more thing here:

Answer 6

A = P(a)*P(c)
B = P(a)*P(d)
C = P(b)*P(c)
D = P(b)*P(d)

Warning do not confuse my A, B, C, D with your answer choices.

Answer 7

So as I mentioned earlier,


P(a) represent the probability Nathan is allergic to Penicillin
P(b) represent the probability Nathan is not allergic to Penicillin
P(c) represent the probability that the test gives a correct result.
P(d) represent the probability the test does give a correct result.

And we have four possibilities to calculate
A = P(a)*P(c)
B = P(a)*P(d)
C = P(b)*P(c)
D = P(b)*P(d)

Keep in mind, they want us to find the probability that Nathan is not allergic to penicillin and the test predicts it. So which should we calculate to find this? A, B, C, or D?