Understanding Bayes' rule

Let us begin by reviewing the Bayes' rule and it's associated terminology, before we start with our project. 

Bayes' rule is used to describe the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, let's say we want to predict the probability a person having diabetes. If we know the preliminary medical test results, we can hope to get a more accurate prediction than when we don't know results of the test. Let's put some numbers around this to understand mathematically:

• 1% of population has diabetes ( and therefore 99% do not)
• Preliminary tests detect diabetes 80% of the time when it is there ( therefore 20% of time we require advanced tests)
• 10% of time preliminary test detect diabetes even when it is not there (therefore 90% of time they...