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Identify the conditioning event
For P(A|B), B is the condition. The numerator is P(A∩B); the denominator is P(B), which must be positive. Rearranging gives P(A∩B) = P(A|B)P(B).
The condition determines the denominator; it is not interchangeable with P(A).
Apply the multiplication rule to a stated case
In a fictional supply model, disruption has probability 25%. Conditional on disruption, shortage has probability 80%. The joint probability of disruption and shortage is therefore 25%×80% = 20%. No independence assumption is needed because the supplied shortage probability is already conditional on disruption.
Identify what the case does not supply
The 80% figure is not the unconditional probability of shortage. To obtain that unconditional probability, the model would also need the shortage probability in the no-disruption state, together with its probability weight.
Check the overlap against the condition
The joint probability cannot exceed the probability of the conditioning event. In this example, 20% is no more than the 25% disruption probability. A purported joint probability of 30% with P(disruption) = 25% would be inconsistent.