- Let us assume that, for some event A there are n possible causes, B1 to Bn.
|For example, event A could be you finding a stray 100 note.|
Event Bi is that note slipping from Bundle 'i'.
- You wish to know P(Bi|A), the probability that one of these causes, the ith, resulted in your observed event, A.
|(Where P(X|Y) is the probability of randomly selecting X, given Y.)|
- Each possible cause is mutually-exclusive and non-overlapping.
- For each of these causes, the probability of observing A is known.
|In other words, if the kth explanation were correct, P(A|Bk) is the probability of observing A.|
- The probability of each causal event, P(Bi), is also known.
|If these causes are equally possible then, given n possible causes, P(Bi)= 1/n, but this is of academic interest, because they cancel out of the equation.|
- Then the probability that event Bi, resulted in your observed event, A, is:
- P(A), is the probability of observing A from any of the bundles, or Σ[P(Bk)P(A|Bk)]