Probability (A2 Unit 4: Applied Mathematics B) — WJEC A-Level Mathematics
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Probability (A2 Unit 4: Applied Mathematics B) explained
Conditional probability evaluates the likelihood of an event A occurring given that another event B has already occurred, denoted P(A|B).
Read the full explanation
Conditioning reduces the relevant sample space from S to B. In tree diagrams, probabilities on secondary branches represent conditional probabilities: the branch for A following branch B represents P(A|B), and the path probability is P(A ∩ B) = P(B) × P(A|B). In two-way contingency tables, conditional probabilities are found by restricting attention to a specific row or column total. On Venn diagrams, P(A|B) is the proportion of region B occupied by the intersection: P(A ∩ B) / P(B).
Your focus
- Calculate conditional probabilities from two-way tables by restricting to row or column totals.
- Construct tree diagrams and calculate compound probabilities along sequential branches.
- Evaluate conditional probabilities using Venn diagrams by comparing intersection to subset area.
Probability (A2 Unit 4: Applied Mathematics B) exam tips
Marking Points
- setting up a tree diagram, Venn diagram, or two-way table representing conditional probability
- identifying the restricted sample space corresponding to the given conditioning event
- evaluating the conditional probability P(A|B) from diagrammatic or tabular frequencies
Examiner Tips
- 💡In two-way tables, circle the conditioning row or column total to use as your denominator.
- 💡Check that the probabilities on each set of branches in a probability tree sum to exactly 1.
Common Mistakes
- confusing P(A|B) with P(B|A) (the fallacy of the transposed conditional)
- dividing by the total sample space size rather than the conditioning subset total in two-way tables