Question

A common blood test indicates the presence of a disease 95% of the time when the disease is actually present in an individual and indicates the absence of disease 95% of the time when the disease is actually absent in an individual. The disease occurs in 1% of the population. What is the probability than an individual has the disease if their blood test is positive? Round the answer to 2 decimal places and enter it into the box below.

Answer 1

Answer:0.161

Step-by-step explanation:

GIven 99% population is disease free and 95 % times it detects  correctly

1% population have disease and test detect 95% time correctly.

Probability that an individual has the disease and test show positive

$P\left [ \frac{have\ disease}{test\ show\ positive}\right ]$

P=$\frac{0.01\times 0.95}{0.99\times 0.05+0.01\times 0.05}$

P=$\frac{0.0095}{0.059}$=0.161