lets assume we have the following data:
$$ \text{Test Result} | \text{Has Disease}\\ 1 | 1\\ 1 | 1\\ 1 | 0\\ 0 | 0\\ 0 | 0\\ 0 | 0\\ 0 | 1\\ 1 | 1\\ 1 | 0\\ 1 | 1 $$
Lets denote P(B) as the probability that one has the disease and P(A) as the probability of a positive test result.
Is it correct to calculate
$$P(B) = \frac{6}{10}$$
and
$$P(A) = \frac{5}{10}$$?
Furthermore, let's evaluate P(B=1|A=1) as the probability of having the disease given that the test result is positive.
Is it correct to say that $$P(B=1|A=1) = \frac{4}{10}$$?
Thanks for any corrections / answers.