This is less of a puzzle and more a write up based on recent news surrounding Angelina Jolie and breast cancer. This write up focusses on the statistical angle and is not meant to prove or disprove conspiracy theories that float around :). An interesting take is mentioned here and all statistics described here borrow from that article.

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (And Everone Else!)

A key point floated around by popular media was that she had an 87% risk of breast cancer because she had the BRCA mutation in her genes. But note, just \(\frac{1}{600}\) actually have that mutation! Even if you did have that mutation, the chances of you eventually getting breast cancer is said to be around \(56\%\). Also note, it is important to understand whether it is

**exactly**that mutation which is causing breast cancer, you have a \(13\%\) chance of getting it anyway (source: Breast Cancer.org). So even if you do test positive for the BRCA mutation, the incremental probability that you will actually develop it is can be calculated as \(56 - 13 = 43\%\). This implies that eventually only \(\frac{600}{0.43} = 1395\) people will actually benefit from the screening. Note how the articles will lead you to believe that you should have a screening done. Once you screen for that gene (and pay for it!) most likely you will come back relieved that you don't have that mutation. This analysis of course discounts false positives and negatives that can come out of the screening process itself which further adds to the chaos. The good news is that if you eat healthy and stay fit you will do well :)

If you are looking to learn the art of probability here are a few good books to own

Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics)

This book is a great compilation that covers quite a bit of puzzles. What I like about these puzzles are that they are all tractable and don't require too much advanced mathematics to solve.

Introduction to Algorithms

This is a book on algorithms, some of them are probabilistic. But the book is a must have for students, job candidates even full time engineers & data scientists

An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!)

Introduction to Probability, 2nd Edition

The Mathematics of Poker

Good read. Overall Poker/Blackjack type card games are a good way to get introduced to probability theory

Bundle of Algorithms in Java, Third Edition, Parts 1-5: Fundamentals, Data Structures, Sorting, Searching, and Graph Algorithms (3rd Edition) (Pts. 1-5)

An excellent resource (students/engineers/entrepreneurs) if you are looking for some code that you can take and implement directly on the job.

Understanding Probability: Chance Rules in Everyday Life A bit pricy when compared to the first one, but I like the look and feel of the text used. It is simple to read and understand which is vital especially if you are trying to get into the subject

Data Mining: Practical Machine Learning Tools and Techniques, Third Edition (The Morgan Kaufmann Series in Data Management Systems) This one is a must have if you want to learn machine learning. The book is beautifully written and ideal for the engineer/student who doesn't want to get too much into the details of a machine learned approach but wants a working knowledge of it. There are some great examples and test data in the text book too.

Discovering Statistics Using R

This is a good book if you are new to statistics & probability while simultaneously getting started with a programming language. The book supports R and is written in a casual humorous way making it an easy read. Great for beginners. Some of the data on the companion website could be missing.

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