Answer:
0.00002 = 0.002% probability of actually having the disease
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Having the disease
Probability of having a positive test:
0.05 of 1 - 0.000001(false positive)
0.99 of 0.000001 positive. So
Probability of a positive test and having the disease:
0.99 of 0.000001. So
What is the probability of actually having the disease
0.00002 = 0.002% probability of actually having the disease