Probability and combinatorics

Basics of probability and combinatorics

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).
Probability with venn diagrams
Probability of compound events. The Addition Rule.
Addition rule for probability
Venn diagrams and the addition rule for probability

Compound probability of independent events using the multiplication rule

See how we can use the multiplication rule to find the compound probability of independent events.
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.
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?
Independent events example: test taking
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.
Coin flipping probability
In this video, we 'll explore the probability of getting at least one heads in multiple flips of a fair coin.
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!
Independent probability
Find probabilities of independent events like flipping a heads and rolling an even number!


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.
Intro to combinations
Sal introduces the basic idea of combinations.
Combination formula
Sal explains the combination formula.
Handshaking combinations
Sal figures out how different combinations of people can shake hands.
Combination example: 9 card hands
Thinking about how many ways we can construct a hand of 9 cards
Introductory combination problems like if you have 5 friends and can pick 2 of them to join you on a boat ride, how many different groups of friends could you take with you?
Permutations & combinations
Permutations and Combinations with overcounting

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.
Probability using combinations
Probability of getting exactly 3 heads in 8 flips of a fair coin.
Probability & combinations (2 of 2)
Making at least 3 out of 5 free throws.
Probability with counting outcomes
The probability of getting exactly 2 heads when flipping three coins. Thinking about this by visualy depicting all of the outcomes.
Getting exactly two heads (combinatorics)
A different way to think about the probability of getting 2 heads in 4 flips
Exactly three heads in five flips
Probability of exactly 3 heads in 5 flips using combinations
Generalizing with binomial coefficients (bit advanced)
Conceptual understanding of where the formula for binomial coefficients come from
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?
Probability with permutations and combinations
Probability questions using permutations and combinations of objects
Mega millions jackpot probability
Probability of winning the Mega Millions jackpot
Birthday probability problem
The probability that at least 2 people in a room of 30 share the same birthday.