Rachel
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Khan Academy on a Stick

Probability and statistics
  • Probability explained

    We give you an introduction to probability through the example of flipping a quarter and rolling a die.

  • Determining probability

    In this example, determine the scenarios that are probable given the rolling of two dice.

  • Finding probablity example

    In order to find the probability of picking a yellow marble from a bag, we have to first determine the number of possible outcomes and how then many of them meet our constraints.

  • Finding probablity example 2

    In this example we are figuring out the probability of randomly picking a non-blue marble from a bag. Again, we'll have to think about the possible outcomes first.

  • Finding probablity example 3

    Now we're working out the probability of randomly selecting a yellow marble from a bag of multi-colored marbles. Let's practice together.

Basic probability

Can I pick a red frog out of a bag that only contains marbles? Is it smart to buy a lottery ticket? Even if we are unsure about whether something will happen, can we start to be mathematical about the "chances" of an event (essentially realizing that some things are more likely than others). This tutorial will introduce us to the tools that allow us to think about random events.

Venn diagrams and adding probabilities

What is the probability of getting a diamond or an ace from a deck of cards? Well I could get a diamond that is not an ace, an ace that is not a diamond, or the ace of diamonds. This tutorial helps us think these types of situations through a bit better (especially with the help of our good friend, the Venn diagram).

  • Compound probability of independent events

    You'll become familiar with the concept of independent events, or that one event in no way affects what happens in the second event. Keep in mind, too, that the sum of the probabilities of all the possible events should equal 1.

  • Coin flipping probability

    In this video, we 'll explore the probability of getting at least one heads in multiple flips of a fair coin.

  • Die rolling probability

    We're thinking about the probability of rolling doubles on a pair of dice. Let's create a grid of all possible outcomes.

  • Free throwing probability

    Our friend and Cleveland Cavalier, LeBron James, asks Sal how to determine the probability of making 10 free throws in a row. Hint: the answer is surprising!

  • Three pointer vs free throwing probability

    Our friend and Cleveland Cavalier, LeBron James, asks Sal if there's a high probability of making three free throws in a row or one three-pointer. Before solving the problem, jot down what you think the answer will be!

  • Probability without equally likely events

    Up until now, we've looked at probabilities surrounding only equally likely events. What about probabilities when we don't have equally likely events? Say, we have unfair coins?

  • Test taking probability and independent events

    Have you ever taken a test and discovered you have no choice but to guess on a couple of problems? In this example problem, we are considering the probability of two independent events occurring.

  • Die rolling probability with independent events

    We hope you're not a gambler, but if you had to bet on whether you can roll even numbers three times in a row, you might want to figure this probability first.

  • Frequency stability property short film

    Can you tell the difference between actions based upon flipping a coin and those based upon blind guessing or simulating randomness? This short video examines the frequency stability property.

Compound, independent events

What is the probability of making three free throws in a row (LeBron literally asks this in this tutorial). In this tutorial, we'll explore compound events happening where the probability of one event is not dependent on the outcome of another (compound, independent, events).

Dependent probability

What's the probability of picking two "e" from the bag in scrabble (assuming that I don't replace the tiles). Well, the probability of picking an 'e' on your second try depends on what happened in the first (if you picked an 'e' the first time around, then there is one less 'e' in the bag). This is just one of many, many type of scenarios involving dependent probability.

Basic set operations

Whether you are learning computer science, logic, or probability (or a bunch of other things), it can be very, very useful to have this "set" of skills. From what a set is to how we can operate on them, this tutorial will have you familiar with the basics of sets!

Old school probability (very optional)

Sal's old videos on probability. Covered better in other tutorials but here because some people actually like these better.