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I've been struggling for a few minutes with this basic thing and I want to make sure I got it right,

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) is

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..

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) is

**immediately**zero when they are disjoint so it never**gets**to 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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