1. HIV test An HIV test gives a positive result with probability 98% when the patient is indeed affected by HIV, while it gives a negative result with 99% probability when the patient is not affected by HIV. If a patient is drawn at random from a population in which 0,1% of individuals are affected... Continue reading

# Statistics for beginners

## Bayes rule exercises: part 4

1. Aircraft emergency locator transmitter An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. The Altigauge Manufacturing Company makes 80% of the ELTs, the Bryant Company makes 15% of them, and the Chartair Company makes the other 5%. The ELTs made by Altigauge have... Continue reading

## Bayes rule exercises: part 3

1. Picking a random student Suppose you have a school with 100 students. Out of those 55 study math (event A), 25 study physics (event B), and 20 study both, as illustrated in the Venn diagram below: Now what’s the probability that a student picked at random studies math GIVEN that we know he studies... Continue reading

## Bayes rule exercises: part 2

1. The Prosecutor's Fallacy Bayes’ theorem often applies when considering the probability that a person is guilty of a crime. Indeed, misunderstanding it leads to what is called the prosecutor’s fallacy – when you interpret the small probability of someone fitting the evidence as a small probability that an accused who does fit the evidence... Continue reading

## Bayes rule exercises: part 1

1. Green and Blue Cabs A cab was involved in a hit-and-run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data: 85% of the cabs in the city are Green and 15% are Blue. A witness identified the cab as Blue. The court... Continue reading