- #1

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Is the law of total probability a theorem or an axiom?

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- #1

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Is the law of total probability a theorem or an axiom?

- #2

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Theorem.

- #3

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If ##B \subset A##, then we may write ##B## as the disjoint union ##B = \bigcup_{n=1}^{N} (B \cap A_n)##, so the axiom gives us ##P(B) = \sum_{n=1}^{N}P(B \cap A_n)##.

Finally, if ##P(A_n) > 0## we

$$P(B) = \sum_{n=1}^{N} P(B|A_n) P(A_n)$$

So, it's a theorem, but quite a simple one: we simply substitute a definition into an axiom.

- #4

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wow!

That is really very clear. :) Thanks.

That is really very clear. :) Thanks.

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