DSOM 5522 -- Fall 2017

Homework #4

Deliverable:

An alternate way to write Bayes’ theorem is:

Where…

•  = Prior probability of event A (this was  in our class session)
•  = Probability of event B, given that event A has happened (this was  in our class session)
•  = Probability of event B, given that A did not happen; this is sometimes written as

A classic example in Bayesian inference regards the likelihood of a woman having breast cancer given a positive result on a mammogram.

Fortunately, the occurrence of breast cancer among young women (below 50) is quite low, about 1.4%.   But the probability of a mammogram accurately detecting cancer, given that the cancer is present, is about 75%.

Work through what the conditional probability is for a woman to have cancer (A) given that she has had a positive mammogram (B)---that is solve for

There is one other piece of data that you need, and that is the ‘false positive’ rate for a mammogram test.  On average, a mammogram will incorrectly suggest that a woman has cancer when she really does not have cancer about 10% of the time.

Turn in to me via direct message on Slack an R Markdown document with that shows your calculations and final result.  Provide a brief (2-3) sentence discussion that accounts for the difference between  and