Introduction to Probability
[Photo by Ella's Dad.]
Throughout history, around the world, people in every culture have enjoyed playing games of chance. Strangely, mathematicians did not begin to study chance and probability until the 17th century.
What Is Probability?
Probability is hard to define. Sometimes probability measures how strongly a person believes a certain statement. In other cases, probability measures how likely it is that a certain event will happen, if the assumptions we make in calculating the probability are true — if the dice are fair, the cards are fully shuffled, the draw is truly random, etc.
Probability doesn’t predict the future: incredibly improbable events happen all the time. You could say that probability is a measure of uncertainty, since if we knew what was going to happen, we wouldn’t need to estimate whether an outcome is likely or not.
How to Calculate Probability
Probability is usually given as a fraction between zero (an impossible event) and one (an event that is absolutely certain to happen) or as a percent between 0% and 100%. Remember, percents are a special type of fraction.
Once you learn how to count, it’s easy to calculate simple probability, IF all the events are all equally likely:
But if the events are not all equally probable, or if you want to know how likely it is that two or more events happen together, or that one event happens given another event, things get tricky. Are the events independent of each other, or does one depend on the other? Are they mutually exclusive? So many things to consider!
I made a tip sheet to help my MathCounts students remember the basics:
Probability Puzzles for You
In the game of Monopoly, what is the chance of taking a ride on the Reading Railroad on your very first turn?
And here are several harder questions about counting and probability:
Learn more about counting and probability with these challenging workbooks from AGMath:
Or explore the Dr. Math archives:
If you prefer video learning, try the excellent series of AoPS Counting & Probability Videos.
Or check out the Khan Academy probability playlist:
To Be Continued…
Read all the posts from the July/August 1999 issue of my Mathematical Adventures of Alexandria Jones newsletter.