Khan Academy on a Stick : Probability and combinatorics

Khan Academy on a Stick

Trigonometry and precalculus

Basic Probability
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An introduction to probability
Example: Marbles from a bag
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The probability of picking a yellow marble from a bag.
Example: Picking a non-blue marble
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Example of figuring out the probability of picking a non-blue marble from a bag.
Example: Picking a yellow marble
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Working out the probability of pulling a yellow marble from a bag of multi-colored marbles.

Basic probability

Probability with Playing Cards and Venn Diagrams
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Probability of compound events. The Addition Rule. Common Core Standard 457 S-CP.7
Addition Rule for Probability
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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
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Probability of particular sequences of flips
Getting At Least One Heads
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Probability of getting at least one heads in multiple flips of a fair coin
Example: Probability of rolling doubles
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Thinking about the probability of rolling doubles on a pair of dice
LeBron Asks: What are the chances of making 10 free throws in a row?
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LeBron James asks Sal how to determine the probability of making 10 free throws in a row
LeBron Asks: What are the chances of three free throws versus one three pointer?
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LeBron James asks Sal Khan if it is easier to make three free throws or one three-pointer.
Frequency Probability and Unfair Coins
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A different way of thinking about probability when we don't have equally likely events
Example: Getting two questions right on an exam
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Probability of two independent events occuring.
Example: Rolling even three times
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Another example showing the probability of rolling an even number three times in a row.

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).

Introduction to dependent probability
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Deciding whether you want to play a game at a strange casino.
Example: Dependent probability
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Thinking about how the probability of an event can be dependent on another event occuring.
Example: Is an event independent or dependent?
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Independent Events 1
Example: Bag of unfair coins
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Example where the probability of an outcome is dependent on which coin you happen to pick
Monty Hall Problem
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Presentation and analysis of the famous Monty Hall Problem

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
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Introduction to permutations
Combinations
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Introduction to combinations
Example: Ways to arrange colors
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Thinking about how many ways you can pick four colors from a group of 6
Example: 9 card hands
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Thinking about how many ways we can construct a hand of 9 cards
Example: Ways to pick officers
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How many ways can we pick officers for our organization?

Permutations and combinations

If 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
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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
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Manually going through the combinatorics to determine the probability of an event occuring
Getting Exactly Two Heads (Combinatorics)
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A different way to think about the probability of getting 2 heads in 4 flips
Probability and Combinations (part 2)
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Making at least 3 out of 5 free throws.
Probability using Combinations
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Probability of getting exactly 3 heads in 8 flips of a fair coin.
Exactly Three Heads in Five Flips
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Probability of exactly 3 heads in 5 flips using combinations
Example: Different ways to pick officers
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Thinking about the different ways we can pick officers in order to find the probability of one situation in particular.
Example: Combinatorics and probability
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Probability of getting a set of cards
Example: Lottery probability
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What is the probability of winning a 4-number lottery?
Mega Millions Jackpot Probability
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Probability of winning the Mega Millions jackpot
Generalizing with Binomial Coefficients (bit advanced)
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Conceptual understanding of where the formula for binomial coefficients come from
Conditional Probability and Combinations
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Probability that I picked a fair coin given that I flipped 4 out of 6 heads.
Conditional Probability (Bayes Theorem) Visualized
Conditional probability visualized using trees.
Birthday Probability Problem
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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.