Conditional Probability

This third chapter on conditional probability begins with a dramatic example. We have a virus test which is extremely good in that if someone has the virus, then there is a 99% chance the test comes back positive and if the person does not have the virus, there is a 99% chance the test comes back negative. Nevertheless when a population of one million people is tested where 1,000 people actually have the virus, if an individual tests positive, there is only a 10% chance he/she has the virus! So we test all the people who tested positive a second time, and then those who test positive a second time have a 90% chance of having the virus. Conditional probability helps us understand why this is so. We meet Kolmogorov’s definition of conditional probability and the important Bayes theorem. We see the Bertrand box problem and the intriguing Monty Hall problem and the related three prisoners problem of Martin Gardner. If we have a 45% chance of living to age 85, what is our chance of living to 85 if we have already reached the age of 75? We introduce Bayesian theory and mention John Maynard Keynes “treatise on probability”.