It is believed that cervical cancer afflicts 2 of a certain

It is believed that cervical cancer afflicts 2% of a certain population of women. A certain screening test for the disease has a sensitivity (P(T+ | D+)) of 90% and a specificity (P(T - | D - )) of 99%

a) Find the probability that a randomly selected women tests positive for cervical cancer.

b) Find the porbability that a randomly selected woman has the disease given that she tests positive.

Solution

a)

P(T+) = P(D+) P(T+|D+) + P(D-) P(T+|D-)

= (0.02)*(0.90) + (1-0.02)*(1-0.99)

= 0.0278 [answer]

b)

P(D+|T+) = P(D+) P(T+|D+) / P(T+) = (0.02)*(0.90)/0.0278

= 0.647482014 [answer]