Question

Given the following statistics for women over the age of 50 entering our medical clinic:

Answer 1

Answer:

P(breast cancer) = 0.01

P(no breast cancer ) = 1-0.01 = 0.99

P(positive | breast cancer)= 0.90

P(positive | no breast cancer ) = 0.08

P(breast cancer | positive ) = $\frac{P(\text{breast cancer}) \times P(\frac{positive}{\text{cancer}})}{P(\text{breast cancer}) \times P(\frac{positive}{\text{cancer}}) + P(\text{ no breast cancer}) \times P(\frac{positive}{\text{no cancer}})}$

Substitute the values :

P(breast cancer | positive ) = $\frac{0.10 \times 0.90}{0.10 \times 0.90+0.99 \times 0.08}$

P(breast cancer | positive ) = $0.531$

Hence the actual probability, if a woman gets a positive test result, that she actually does have breast cancer is 0.531