Probability

False Positives… Test Accuracy

Given

• 1/500 people have HIV• HIV test is 99% accurate

What probabilities do you know?Consider the “nots”

q = 1-p = p’

• P(HIV) = 1/500• P’(HIV) = 1-(1/500) = 499/500

• Test 99% accurate means P(test positive/ have HIV) = .99 P(test negative/don’t have)

Set up a tree !

Add probabilities

.002

.998

.99

.99

.01

.01

Do all

.002

.998

.99

.99

.01

.01

P(have HIV and test +)?.002*.99= .00198

All add up to 1

Prob(B/A) = Prob(B)Prob(B/A)= P(AandB)/P(A)

P(Not HIV and Test +) / Prob(Test Postive)

= .00998/( .00998+.00198) =

How can it be that high?