# Bayes Theorem probability of getting two positive results?

In a certain clinic $1$% of patients have a certain virus.

If a test is carried out on a positive patient, there is a $5$% probability that the test will give a false result.

If a test is carried out on a negative patient, there is a $10$% probability that the test will give a false result.

A) What is the probability that a patient has the virus given a positive result?

B) Suppose a second test is carried out on the same patient, what is the probability of two positive results?

I'm stuck with part B

Because the testing is independent (The outcome of the first test doesn't affect the outcome of the second test) does this mean that the probability of getting two positive results is the probability of getting one positive result times $2$?

• If $p$ is the probability of a positive result then the probability of twice a positive result by two independent tests is not $2p$ (as you suggest) but is $p\times p$. – drhab May 16 '18 at 9:35
• @drhab Great, I was on the right track anyway thanks for you answer! – Darragh O'Flaherty May 16 '18 at 9:48

• So the answer from part a is $$\frac{0.0095 * 0.01}{0.1085}$$. So the answer would be $$\frac{(0.0095) * (\frac{19}{21700})}{0.1085}$$ – Darragh O'Flaherty May 16 '18 at 9:40