Find an x such that mutually exclusive events are to disjoint sets what independent events are to x

Paxton Hoffman

Paxton Hoffman

Answered question

2022-07-20

Find an x such that mutually exclusive events are to disjoint sets what independent events are to x

Answer & Explanation

Brendon Bentley

Brendon Bentley

Beginner2022-07-21Added 11 answers

In pure set theoretic terms, there is no notion of measure, so it is difficult to talk about events being independent. Disjoint events are those with no overlap, and you don't need a notion of measure to say that two sets have no elements in common.
To capture the notion of independence, we would have to say that the proportion of set A that overlaps with set B is the same as the proportion of the universal set that set B occupies. In pure set theory, there's not really any need for talking about sets in this way, unless we're doing probability.

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