4 What is the probability that a random person who tests pos

4. What is the probability that a random person who tests positive for a certain skin disease, actually has the disease, if it is known that: 1% of the population has the disease; and 95% of those who have it test positive for it; and 2% of those who do not have it test positive for it?

Solution

                         Has disease            no disease     Total

Positive                 0.95                           1.98          2.93

Negative                0.05    97.02    97.07                   

Total                         1                           99                100

Prob for a random person tested positive actually has the disease =

Prob tested positive and has disease/prob has disease = 0.95