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Prove using only the axioms of probability that if A and B are events and A...

Prove using only the axioms of probability that if A and B are events and A ⊂ B, then P(Ac ∩ B) = P(B) − P(A).

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Answer #1

Now we know by the additive theorem of probability:

Now A ⊂ B i.e A is a subset of B which means the entire event A is contained in event B which means

Hence

Hence proved.

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!

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