# Probability

## Should Rare Events Surprise Us?

(Archive Question of the Week) We often receive questions saying something like, “My wife has the same birthday as my son-in-law, whose dog has the same name as my wife’s brother, … ,” and asking us to calculate how likely it is that this would happen. Sometimes it is simply impossible to answer (without, say, looking up …

## How Do You Know That Events Are Equally Likely?

(Archive Question of the Week) Having recently discussed a couple different issues that touched on the relationship of math to reality, I was reminded of this old favorite – a  question that is not asked often enough, and reveals some of the “dirty little secrets” behind math. Math is not reality; it is often used …

## Averages, Probability, and Reality

(Archive Question of the Week) Recently I discussed the definition of the median of a data set, pointing out how it needs refinements that are not often discussed. In searching for questions in our archive on that topic, I ran across a discussion of an opposite issue: the breadth of the general term “average”, which …

## WHY Do We Add or Multiply in Probability?

Last time, we discussed how you know whether to add or multiply (or something else) in compound probability problems (like finding the probability that you will flip heads and roll an even number). But as I’ve said before, it’s often easier to remember a formula if you know why it is what it is. I’ll …

## When Do I Add or Multiply in Probability?

Probability is a subject in which it can be quite difficult to see at a glance what method to use. There are many ways in which its ideas can be combined. Two principal ways are “or” and “and”: What is the probability that I draw an ace or a spade? How about an ace and …