I've been struggling for a few minutes with this basic thing and I want to make sure I got it right,(adsbygoogle = window.adsbygoogle || []).push({});

given A, B being disjoint,

We know that P(A and B) = 0

However, if they are independent then P(A and B) = P(A) x P(B)

Then if P(A) is [STRIKE]finite[/STRIKE] non zero and P(B) is [STRIKE]finite[/STRIKE] non zero, how could P(A and B) be zero?

My explanation is that the mistake in that reasoning is that P(A and B) isimmediatelyzero when they are disjoint so it nevergetsto be tested for P(A) x P(B).

So in that case P(A) x P(B) is completely meaningless and it has no reason to be calculated at all: "Yeah, the product produces a number, but it's completely useless. If you started with P(A and B) you would immediately derive it's zero without reaching that calculation."

Is that assessment correct?

Then again I wonder if that product has any meaning at all that could be useful..

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# Multiplying the probabilities of two disjoint sets.

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