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Treat the figures as a stated learning model
The event is a control weakness and the evidence is an exception flag. The model supplies the prior and both evidence likelihoods. It does not establish an actual audit result or determine what action a real compliance team should take.
Calculate the probability of a flag under both states
| State | Prior weight | Flag likelihood | Joint state-and-flag probability |
|---|---|---|---|
| Weakness | 35% | 75% | 26.25% |
| No weakness | 65% | 15% | 9.75% |
| Total flag probability | 36% |
Divide by the total flag probability
The weakness-and-flag branch accounts for 26.25% of the complete model. Among the 36% assigned to a flag, the weakness share is 26.25/36 = 72.9167%. The remaining share, 27.0833%, belongs to no weakness despite a flag.
Distinguish three different percentages
35% is the prior before the flag. 75% is the likelihood of a flag given weakness. Approximately 72.9167% is the posterior probability of weakness given a flag. Reusing the likelihood as the posterior reverses the conditioning direction.