Confused on how to apply Bayes Th. to this problem.
You have a machine that can identify a disease in 75% of cases, and in 95% of cases the machine is able to correctly indicate that a person does NOT have a disease. What is the probability of a machine incorrectly saying a person has a disease when they do not, and what is the probability of the machine incorrectly saying a person does not have a disease when they actually do?
Assume M stands for the machines predictability. Assume D stands for a person having the disease.
P(M)=0.75 which means the machine correctly predicts 75% of the time, P(M')=0.25 which means the machine incorrectly predicts 25% of the time.
P(M|D')=0.95 meaning a person does not have a disease and the prediction is positive.
I need to first find P(M'|D) is the probability of a person having the disease but the prediction is wrong. I then need to find P(M'|D') which is person not having disease and prediction is wrong.
I am stuck here. Is my thought process correct? Do I not need to have information of P(D) to proceed?