Question

Approximately 1% of women aged 40-50 have breast cancer. A woman with breast cancer has a 90% chance of a positive test from a mammogram, while a woman without has a 10% chance of a false positive result. What is the probability a woman has breast cancer given that she just had a positive test

Answer 1

We define following events first.

• denotes the event that a woman has breast cancer.
• denotes the event that a woman tests positive from a mammogram.

From given data we have,

• 
• 
• 

Using Bayes' theorem required conditional probability is given by