Question: One in one hundred and forty people have a particular disease. A diagnosis test gives a false positive 2 % of the time, and a false negative 8% of the time. We took 3 tests simultaneously and got 1 negative and 2 positive tests.
- What is the probability that we have disease?
- What will be the probability if we took 3 sequent tests: a) one negative first and 2 positives after? b) vice versa?
I think I nanaged to solve 1st part of task with simultaneously testing:
A - we have disease B - positive test C - negative test D - 1 negative and 2 positive tests
P(A/D) = P(D/A) * P(A) / P(D) P(D) = 1/140 * 92% * 92% * 8% + 139/140 * 98% * 2% * 2% = 0.09% P(D/A) = 92% * 92% * 8% = 6.8% P(A/D) = 6,8% * 1/140 / 0,09% = 55.6% - the answer on 1st question
Is it correct? I don't understand how to solve part with sequent testing.