# Geometric intuition of Bayes' Theorem

## Motivation

Q1 → *1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?*

**ALERT** - Solving this question using a calculator and Bayes’ Theorem is easy. What I challenge you to do is without picking up your calculator or writing a single digit, estimate the answer upto an accuracy of let us say $\pm 5\%$. And yes, you are allowed to use pen-paper but only for diagrams.