Conditional probability
P(A|B) = P(A ∩ B) / P(B). The probability of A given B has already happened. Higher tier.
Higher-tier extension. Often appears with tree diagrams (without replacement) or Venn diagrams. Read ‘A given B’ carefully — it restricts the sample space to B's outcomes.
Worked examples
Bag 5R 3B; one drawn (red); P(2nd red | 1st red) = 4/7.
P(rain | cloud) = P(rain ∩ cloud) / P(cloud).
If A and B are independent, P(A|B) = P(A).
Frequently asked questions
Order matters?
Yes — P(A|B) is generally NOT equal to P(B|A). Bayes' theorem links them but is A-Level.
How does it appear in tree diagrams?
The second-stage branch probabilities ARE conditional probabilities given the first-stage outcome.