Probability
Combine conditional probability with restricted, repeated and circular arrangements under an explicit sampling convention.
More
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Find this activity in your course
Before you begin
Combine conditional probability with restricted, repeated and circular arrangements under an explicit sampling convention.
Learning goals
- Use counting principles, permutations and combinations
- Calculate and interpret conditional probabilities
- Calculate event probabilities from an explicit sample space
- Distinguish independence from mutual exclusivity
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).
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Counting and conditional probabilityChoose counting structures, interpret event regions and conditional trees, and use the observed condition as the reference set.
- Repeated and circular arrangementsCount restricted repeated and circular outcomes, then condition probabilities on the actual selection and seating experiment.