Question

It has been found that 0.01% of the world population has a certain disease. If a person has the disease, there is a 95% chance they will test positive for the disease. If a person does not have the disease, there is a 5% chance they will test positive for the disease. (a) What is the probability that a person chosen at random will both have the disease and test positive? 0.000095 (or 9.5 x 10-5) (b) What is the probability that a person chosen at random will both not have the disease and test positive? 0.049995

Answer 1

let probability of having disease =P(D) and test positive =P(T)

here P(D) =0.0001 ; P(T|D) =0.95 ; P(T|D^c)=0.05

a)P(peson have both diease and test positive) =P(D n T) =P(D)*P(T|D) =0.0001*0.95 =0.000095

b) P(having not both disease and test positive) =P(D^c)*P(T|D^c) =(1-0.0001)*0.05=0.049995

( please revert fr any clarification required)