Probability

This course contains 9 segments:

Basic theoretical probability

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.

Probability using sample spaces

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.

Basic set operations

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.

Experimental probability

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).

Randomness, probability, and simulation

The probability of an event gives us an idea of how often that event will occur in a long series of trials. We'll learn how to set up and carry out simulations to estimate theoretical probability using experimental probability.

Addition rule

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.

Multiplication rule for independent events

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.

Multiplication rule for dependent events

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 and independence

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.