Compound probability?

Do you mean the probability of multiple events happening (joint/probability of intersections) or the probability of at least one happening (union)? Or something else like conditional probability?

Here’s a quick primer you can use:

- Joint (intersection) probability:
- For two events A and B: P(A ∩ B) = P(A) × P(B|A) = P(B) × P(A|B)
- If A and B are independent: P(A ∩ B) = P(A) × P(B)
- For n events: P(A1 ∩ A2 ∩ … ∩ An) = P(A1) × P(A2|A1) × P(A3|A1,A2) × …

- Union probability (at least one occurs):
- P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
- If A and B are disjoint: P(A ∪ B) = P(A) + P(B)

- Conditional probability:
- P(B|A) = P(A ∩ B) / P(A)
- Bayes’ theorem: P(A|B) = [P(B|A) × P(A)] / P(B)

Quick examples:
- Two fair coins: probability both show heads = (1/2) × (1/2) = 1/4.
- Two cards without replacement from a standard deck being red: P(first red) = 26/52 = 1/2; P(second red | first red) = 25/51; total = (1/2) × (25/51) ≈ 0.245.
- At least one of two events A, B: P(A ∪ B) = 1 − P(A′ ∩ B′). For independent events, P(A ∪ B) = P(A) + P(B) − P(A)P(B).

If you have a specific problem or numbers, share them and I’ll work through it step by step.