We have seen a number of questions recently about combinatorics: the study of methods for counting possibilities. These topics are studied at all levels of mathematical education, from elementary (where they might just be called counting) to high school (where they are often learned along with probability) to college (where they are part of “discrete …
(A new question of the week) A recent question about probability has ties to Venn diagrams, tables, and Bayes’ Theorem. Questions about answering multiple-choice questions are common; this one offers a twist that provided opportunity to discuss several important concepts. Here is the initial question, from August: On a multiple choice question, only one answer is …
(An archive question of the week) One of the discussions we looked at last time involved rolling three dice and getting at least one six. I didn’t go into detail on the calculation there; but I found another place where we discussed it at length. We’ll look at that here. A wrong way and a …
Probability seems simple enough to many people that it can fool them into wrong conclusions. We have had many questions that involve the “Gambler’s Fallacy”, both from people who naively assume it without thinking, and from some who defend it using technical ideas like the Law of Large Numbers. The Gambler’s Fallacy Here is a …
(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 …
(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 …
(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 …
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 …
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 …