Probability Problem

[omair_bba]

Q. A certain disease occurs in 1 person out of every 101 people.A test for disease is 100% accurate for patients with the disease and 99% accurate for patients without it. That is it gives a 'false positive' 1% of the time even if the person tested doesn't have the disease.If you take this test and it returns a positive result, what is the probability that you have the disease ?

A) 1
B) 0.99
C) 0.95
D) 0.50
E) 0.01

Answer = D .

Please explain answer too !

Thankx...

[Ian Stewart]

It's a pure ratio problem, so we can solve it just by picking a number. Imagine you have 101 people. Then 1 person has the disease, and 100 do not. If they all take this test, the test will correctly identify the 1 person who has the disease. For the 100 people who do not, the test will correctly report that 99 do not have the disease. But for 1 of these 100 people, the test will give a 'false positive'; the test will report that the person has the disease when he or she does not. So of our 101 people, 2 will test positive, but only 1 will have the disease, so 1/2 of all people who test positive actually have the disease.