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Unit: Probability and combinatorics

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Possible mastery points

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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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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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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"At least one" probability with coin flipping
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Free-throw probability
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Three-pointer vs free-throw probability
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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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Dependent probabilityGet 3 of 4 questions to level up!

Quiz 1

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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!

Quiz 2

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Unit test

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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!