# Probability

Contents

Probability tells us how often some event will happen after many repeated trials. This topic covers theoretical, experimental, compound probability, permutations, combinations, and more!

Basic theoretical probability is mapping out how many outcomes are possible and seeing how many of those outcomes relate to the probability we're trying to find.

A sample space shows every possible equally likely outcome in some chance process like flipping a coin or rolling a pair of dice. Sample spaces can help us find the probability of certain events like rolling doubles or getting heads twice in three flips.

Experimental probability estimates the theoretical probability of an event by repeating trials over and over and keeping track of what percent of the trials the event actually happens. For example, spin a coin over and over and see if it lands on "heads" 50% of the time (you may be surprised).

Basic set operations and set notation are the language of more advanced probability and logic. Learn how to express intersections, unions, complements, and subsets symbolically.

The addition rule says that we can find the probably of one event or another event happening by adding their probabilities, but we have to be careful and subtract the overlapping probability of both events happening at the same time.

The multiplication rule says that we can multiply the probability of independent events to find the probably of all of the events happening. You'll learn how to find the probability of getting three heads in a row when tossing a coin, or a basketball player making five shots in a row.

The multiplication rule works for dependent events, we just have to adjust each probability based on the previous event occurring. You'll learn how to find the probability of events like drawing two red cards in a row from a deck of cards.

Conditional probability is the likelihood of some event occurring given some other event has occurred. You'll learn how to calculate conditional probability intuitively and with a formula called Bayes' theorem.

The counting principal tells us that we can multiply the number of choices together to get a count of the total possible outcomes. If you own two pairs of pants and three shirts, then you have six possible outfits.

Permutations count how many ways you can select and arrange items or people from a larger group. For example, how many different ways can we award a gold, silver, and bronze medal to three runners out of a group of 10?

Combinations are similar to permutations. Combinations count how many ways we can pick a group of people or things from a larger group where order doesn't matter. For example, how many different groups of 3 people can a company with 10 employees send on a business trip?

Once we understand the counting principle, permutations, and combinations, we can use those concepts to calculate some pretty advanced probabilities!