Probability

This course is a part of High school statistics, a 7-course Topic series from Khan Academy.

Few things are certain in life. Probability gives us an idea of the likelihood or unlikelihood of different outcomes.

This course contains 10 segments:

Probability basics

Flip a quarter a hundred times. What's the probability that it will turn up heads? Tails? Even if we are unsure about whether something will happen, we can start to be mathematical about the "chances" of an event (essentially realizing that some things are more likely than others) occurring. This tutorial will introduce us to the tools that allow us to think about random events and the logic behind comparing, judging, and finding the probabilities of those events.

Counting with permutations

You want to display your Chuck Norris dolls on your desk at school and there is only room for five of them. Unfortunately, you own 50. How many ways can you pick the dolls and arrange them on your desk?

Counting with combinations

You are already familiar with calculating permutation ("How many ways could 7 different people sit in 4 different seats?"). But what if you didn't care about which seat they sat in? What if you just cared about which 4 people were in the car? Or put another way, you want to know how many combinations of 4 people can you stick in the car from a pool of 7 candidates. Or how many ways are there to choose 4 things from a pool of 7? Look no further than this tutorial to answer your questions.

Probability with counting, permutations, combinations

This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better "investments" than spending all your money on the Powerball Lottery.

Multiplication rule for independent events

What’s the probability that three people were all born on the same day of the week? How likely is a basketball player to make three shots in a row? In this tutorial, we’ll see that multiplying probabilities can be quite useful.

Multiplication rule for dependent events

What’s the probability of drawing two aces in a row from a deck of cards? Getting an ace on the first card changes the probability for the second card. This tutorial covers how we can deal with that when multiplying probabilities.

Addition rule for probability

What’s the probability of picking a card and getting a jack or a heart? What’s the probability that someone owns a laptop or a smartphone? This tutorial will show how we can add probabilities to solve these types of problems.

Conditional probability

Given someone likes cheese, what’s the probability they also like pizza? Knowing something can change what we know about the probability of something else. This tutorial on conditional probability covers how to find probability based on some known condition.

Simulation and randomness

Drawing names from a hat is fun, and so is calculating probability with formulas, but there are other options. This tutorial covers how we can use simulations and random digits to get samples and find probabilities.

Expected value

Will a basketball player score more points over time from a two point shot or a three point shot? How much money can we expect to win back if we play the lottery? This tutorial on expected value will help us answer these types of questions.