Question

One percent of the population suffers from a certain disease. There is blood test for this disease, and it is $99\%$ accurate, in other words, the probability that is gives the correct answer is $0.99$, regardless of whether the person is sick or healthy. A person takes the blood test, and the result says that he has the disease. The probability that he actually has the disease, is?

• A. $0.99\%$
• B. $25\%$
• C. $50\%$
• D. $75\%$

Answer 1

The correct option is C $50\%$

A be the event of having the disease.

B be the event of testing positive.

$P\left(A\right)=0.01$

$P\left(B\right)=P\left(B/A\right)P\left(A\right)+P\left(B/notA\right)P\left(notA\right)$

$P\left(B\right)=0.01\ast 0.99+0.01\ast 0.99=0.0198$

$P(A\cap B)=0.99\ast 0.01$

$P\left(A/B\right)=\frac{P(A\cap B)}{P\left(B\right)}$

$⟹\frac{0.99\ast 0.01}{0.0198}$

=$0.5$ or $50\%$