a. What’s the probability of having a peanut allergy?

P (peanut allergy) = 0.023

b. Find the probability that the test results in a positive outcome

P(+ result): P(+ result/allergy) + P(+ result/no allergy) = (0.023x0.80) + (0.977x0.10) = .1161

c. Given that the test results in a positive outcome, what is the probability of having a peanut allergy?

P(+ result/allergy) = P(+result / allergy) / P(+result) = .0184/.1161 = .1585

This is what I have so far, but the last time I did a similar problem, my teacher said that part c. is not conditional, and that you have to multiply across the branches. I'm not sure how to do that part. What is the correct way to do part c.? Thanks!