When to use it
Use conditional reasoning for decision trees and related risk events.
When to be cautious
Do not multiply marginal probabilities unless independence is justified.
Apply it
P(A given B) = P(A and B) / P(B)
Requires P(B) > 0. Under independence only, P(A and B) = P(A) × P(B). Mutually exclusive positive-probability events are not independent.
- Define events and the population or time horizon.
- Identify which probability statements are conditional.
- Check that mutually exclusive exhaustive outcomes sum to certainty.
An example in practice
Two suppliers rely on the same port. Their delivery failures should not automatically be treated as independent.
Source & credit
Standard mathematical statistics; the handbook is an authoritative technical reference, not a claim of sole origin.
NIST/SEMATECH: statistical methods
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