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Topic · Grades 7 to 12

Probability

Measuring how likely something is.

4 subtopics53 lessons
1

Compound events

14 lessons

Two or more things happening, together or in sequence.

1.1Compound events
1.2Tree diagrams and organized listsMath 7
1.3Dependent events and drawing without replacementMath 7
1.4Independent events and the multiplication ruleMath 7
1.5Union and intersection of eventsAlgebra 2
1.6Mutually exclusive events and the addition ruleAlgebra 2
1.7The general addition ruleAlgebra 2
1.8At least one problemsAlgebra 2
1.9The general multiplication ruleAlgebra 2
1.10Conditional probability
1.11Joint and marginal probabilityAlgebra 2
1.12Finding a conditional probabilityAlgebra 2
1.13The law of total probabilityAlgebra 2
1.14Bayes' ruleAlgebra 2
2

Counting

11 lessons

How many ways, without listing them all.

2.1Counting
2.2The fundamental counting principleMath 7
2.3Arrangements and factorialsAlgebra 2
2.4PermutationsAlgebra 2
2.5CombinationsAlgebra 2
2.6Pascal's triangleAlgebra 2
2.7The binomial theoremAlgebra 2
2.8Counting with restrictionsAlgebra 2
2.9Combinations with repetition: stars and barsDiscrete Mathematics and Proof
2.10Inclusion-exclusion for three or more sets, and derangementsDiscrete Mathematics and Proof
2.11Probability with counting formulasAlgebra 2
3

Basic probability

14 lessons

Counting what can happen, and the fraction of it you want.

3.1Basic probability
3.2Chance in words and the 0 to 1 scaleMath 7
3.3Complements and probabilities that add to oneMath 7
3.4Designing a simulationMath 7
3.5Geometric probabilityMath 7
3.6Listing a sample space: lists and tablesMath 7
3.7Probability models: equally likely or notMath 7
3.8Probability of an eventMath 7
3.9Sample spaces, outcomes and eventsMath 7
3.10What randomness meansMath 7
3.11Experimental probability and relative frequencyMath 7
3.12OddsAlgebra 2
3.13The law of large numbers and the gambler's fallacyMath 7
3.14Running a simulation and estimating a probabilityMath 7
4

Random variables

14 lessons

A number attached to each outcome, and the distribution of those numbers.

4.1Cumulative probabilityStatistics
4.2Expected valueStatistics
4.3Mean and standard deviation of a binomialStatistics
4.4Mean and standard deviation of a geometric random variableStatistics
4.5Random variables
4.6Random variables and probability distributionsStatistics
4.7The binomial distribution
4.8The binomial probability formulaStatistics
4.9The binomial settingStatistics
4.10The geometric distributionStatistics
4.11Variance and standard deviation of a random variableStatistics
4.12Shape of a binomial and the normal approximationStatistics
4.13Linear transformations of a random variableStatistics
4.14Combining random variablesStatistics