Bayesian rule and false positive cases

Suppose in a residential area, a rare disease infects 1 of people ...

And suppose the disease has a good test: if someone is infected with the disease, the test results are 99% likely to be positive. On the other hand, this test also produces some false positives. 2% of the patients who were infected were also tested positively. And you just tested positive, how likely are you to infect the disease?

We work according to two events:

A: Patients get the disease

B: Positive test results

The accuracy of the test results is as follows:

P (A) =0.001--1‰ people get the disease

P (b| A) =0.99--the probability that the person who really got the disease tested positive was 99%.

P (b| A) =0.02--people who didn't have the disease. The probability of a false positive test result is 2%.

Then P (a| B) How much is it? What is the probability that the test results are positive for the infection?

P (a| B) = P (a)/(P (a) *p (b| A) + (1-p (a)) *p (b| a)) = 0.001/(0.001*0.99+ (1-0.001) *0.02) =0.0472

　　Despite the high accuracy of the tests, in fact, less than 5% of those who tested positive had the disease, and this was a false-positive paradox.

Bayesian rule and false positive cases