About this topic
Before you begin
Combine conditional probability with restricted, repeated and circular arrangements under an explicit sampling convention.
Learning goals
- Calculate ordered selections of distinct objects
- Calculate unordered selections of distinct objects
- Calculate event probabilities from finite uniform counts
- Determine conditional probabilities from finite uniform counts
- Classify finite-count event relationships with supporting count products
- Use counting principles, permutations and combinations
- Calculate and interpret conditional probabilities
- Calculate event probabilities from an explicit sample space
- Distinguish independence from mutual exclusivity
- Calculate linear arrangements of indistinguishable types
- Calculate circular arrangements of distinct objects
Syllabus statements covered
- Include: addition and multiplication principles for counting; permutations nPr and combinations nCr; arrangements of objects in a line or circle, including repetition and restrictions; addition and multiplication of probabilities; mutually exclusive and independent events; tables of outcomes, Venn diagrams, tree diagrams, permutations and combinations to calculate probabilities; conditional probabilities in simple cases; P(A′) = 1 − P(A); P(A ∪ B) = P(A) + P(B) − P(A ∩ B); P(A|B) = P(A ∩ B)/P(B).
- Include: addition and multiplication principles for counting; permutations nPr and combinations nCr; arrangements of objects in a line or circle, including repetition and restrictions; addition and multiplication of probabilities; mutually exclusive and independent events; tables of outcomes, Venn diagrams, tree diagrams, permutations and combinations to calculate probabilities; conditional probabilities in simple cases; P(A′) = 1 − P(A); P(A ∪ B) = P(A) + P(B) − P(A ∩ B); P(A|B) = P(A ∩ B)/P(B).
Choose a lesson
Work through them in order.
- Not startedCounting and conditional probabilityNextChoose counting structures, interpret event regions and conditional trees, and use the observed condition as the reference set.
- Not startedRestricted line arrangementsNextCount lines of distinct objects with together, apart, position and order restrictions, then turn the counts into probabilities.
- Not startedRepeated and circular arrangementsNextCount restricted repeated and circular outcomes, then condition probabilities on the actual selection and seating experiment.