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Probability and combinatorics

Basic probability

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Intro to theoretical probability
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Simple probability: yellow marble
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Simple probability: non-blue marble
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Practice
Simple probabilityGet 5 of 7 questions to level up!

Venn diagrams and the addition rule

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Probability with Venn diagrams
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Addition rule for probability
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Compound probability of independent events using diagrams

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Die rolling probability
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Probability with counting outcomes
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Compound events example with tree diagram
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Practice
Probabilities of compound eventsGet 3 of 4 questions to level up!

Compound probability of independent events using the multiplication rule

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Compound probability of independent events
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Probability without equally likely events
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Independent events example: test taking
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Die rolling probability with independent events
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Coin flipping probability
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Free-throw probability
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Three-pointer vs free-throw probability
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Practice
Independent probabilityGet 3 of 4 questions to level up!

Dependent events

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Dependent probability introduction
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Dependent probability: coins
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Dependent probability example
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Independent & dependent probability
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The Monty Hall problem
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Practice
Dependent probabilityGet 3 of 4 questions to level up!

Permutations

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Factorial and counting seat arrangements
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Permutation formula
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Possible three letter words
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Zero factorial or 0!
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Ways to arrange colors
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Ways to pick officers
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Practice
PermutationsGet 3 of 4 questions to level up!

Combinations

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Intro to combinations
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Combination formula
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Handshaking combinations
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Combination example: 9 card hands
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Practice
CombinationsGet 3 of 4 questions to level up!
Permutations & combinationsGet 5 of 7 questions to level up!

Probability using combinatorics

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Probability using combinations
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Probability & combinations (2 of 2)
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Probability with counting outcomes
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Getting exactly two heads (combinatorics)
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Exactly three heads in five flips
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Generalizing with binomial coefficients (bit advanced)
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Example: Different ways to pick officers
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Example: Combinatorics and probability
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Example: Lottery probability
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Mega millions jackpot probability
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Birthday probability problem
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Practice
Probability with permutations and combinationsGet 3 of 4 questions to level up!

About this unit

Probability and combinatorics are the conceptual framework on which the world of statistics is built. Besides this important role, they are just fascinating and surprisingly fun!