# Probability of a disease test

• Sep 18th 2009, 03:09 AM
kin
Probability of a disease test
Suppose that there is a blood test for a particular disease.
The probability of giving positive result at the presence of the diseae is 85%,
while the probability of giving negative result at the absence of the disease is 95%.

Accordng to the previous experience, 7% of the patients who have undergone the test have that disease.

a) What's the probability that the patient has the disease if the test gives positive result?

b) Suppose that the patient has taken the test twice. The 2 tests are taken in two labs seperately under similar lab conditions.
What's probability that the patient has the disease both tests give positive results?
• Sep 18th 2009, 06:40 AM
mr fantastic
Quote:

Originally Posted by kin
Suppose that there is a blood test for a particular disease.
The probability of giving positive result at the presence of the diseae is 85%,
while the probability of giving negative result at the absence of the disease is 95%.

Accordng to the previous experience, 7% of the patients who have undergone the test have that disease.

a) What's the probability that the patient has the disease if the test gives positive result?

b) Suppose that the patient has taken the test twice. The 2 tests are taken in two labs seperately under similar lab conditions.
What's probability that the patient has the disease both tests give positive results?

Pr(+ve | D) = 0.85.
Pr(-ve | D') = 0.95.
Pr(D) = 0.07.

I drew a tree diagram.

a) From the tree diagram: $\displaystyle \Pr(D \, | \, +ve) = \frac{(0.07)(0.85)}{(0.07)(0.85) + (0.93)(0.05)}$.