The prevalence of breast cancer is 1 for women over age 40 A

The prevalence of breast cancer is 1 for women over age 40. A widely used test, mammography, gives a positive result in 10 of women without breast cancer, and in 80 of women with breast cancer. What is the probability that a woman in this age class who tests positive actually has breast cancer.

Solution

The prevalence of breast cancer is 1 for women over age 40. A widely used test, mammography, gives a positive result in 10 of women without breast cancer, and in 80 of women with breast cancer. What is the probability that a woman in this age class who tests positive actually has breast cancer.

P(D)=1/40

P(D^C)=39/40

P(+/D)=0.8

P(+/D^C)=0.1

We are using Bayes theorem

P(D/+) =P(+/D)P(D)/ ( P(+/D)P(D)+ P(+/D^C)P(D^C))

=1*0.8/40 /( 1*0.8/40 +39*0.1/40)

=0.02/0.1175

=0.1702

The required P=0.1702