Khan Academy on a Stick
Probability and combinatorics
Basics of probability and combinatorics
-
Probability explained
We give you an introduction to probability through the example of flipping a quarter and rolling a die.
-
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
-
Probability with playing cards and Venn diagrams
Probability of compound events. The Addition Rule. Common Core Standard 457 S-CP.7
-
Addition rule for probability
Venn diagrams and the addition rule for probability
Venn diagrams and the addition rule
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.
-
Compound events example with tree diagram
-
Compound events example using diagram
-
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.
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 introduction
Let's get you started with a great explanation of dependent probability using a scenario involving a casino game.
-
Dependent probability example
We're thinking about how the probability of an event can be dependent on another event occuring in this example problem.
-
Independent or dependent probability event?
This time around we're not going to tell you whether we're working on a dependent or independent probability event problem. You tell us!
-
Dependent probability example 2
It's important to practice these probability problems as they get more complex eventually. Take a stab on this one...with our help, of course.
-
Probability and the Monty Hall problem
Here we have a presentation and analysis of the famous thought experiment: the "Monty Hall" problem! This is fun.
Dependent events
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.
-
Permutations
Introduction to permutations
-
Combinations
Introduction to combinations
-
Example: Ways to arrange colors
Thinking about how many ways you can pick four colors from a group of 6
-
Example: 9 card hands
Thinking about how many ways we can construct a hand of 9 cards
-
Example: Ways to pick officers
How many ways can we pick officers for our organization?
Permutations and combinations
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? What if you don't what order they are in or how they are posed (okay, of course you care about their awesome poses)?
-
Example: Probability through counting outcomes
The probability of getting exactly 2 heads when flipping three coins. Thinking about this by visualy depicting all of the outcomes.
-
Example: All the ways you can flip a coin
Manually going through the combinatorics to determine the probability of an event occuring
-
Getting exactly two heads (combinatorics)
A different way to think about the probability of getting 2 heads in 4 flips
-
Probability and combinations (part 2)
Making at least 3 out of 5 free throws.
-
Probability using combinations
Probability of getting exactly 3 heads in 8 flips of a fair coin.
-
Exactly three heads in five flips
Probability of exactly 3 heads in 5 flips using combinations
-
Example: Different ways to pick officers
Thinking about the different ways we can pick officers in order to find the probability of one situation in particular.
-
Example: Combinatorics and probability
Probability of getting a set of cards
-
Example: Lottery probability
What is the probability of winning a 4-number lottery?
-
Mega millions jackpot probability
Probability of winning the Mega Millions jackpot
-
Generalizing with binomial coefficients (bit advanced)
Conceptual understanding of where the formula for binomial coefficients come from
-
Conditional probability and combinations
Probability that I picked a fair coin given that I flipped 4 out of 6 heads.
-
Conditional probability warmup
Conditional probability visualized using trees.
-
Birthday probability problem
The probability that at least 2 people in a room of 30 share the same birthday.
Probability using combinatorics
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 poring all your money into the Powerball Lottery.