Exercise 1.44

Let A and B be events. The difference B − A is defined to be the set of all elements of B that are not in A. Show that if A ⊆ B, then

P(B − A) = P(B) − P(A)

directly using the axioms of probability.

Answers

Since B = (B − A) ∪ A, P(B) = P(A) + P(B − A) by the second axiom of probability. Rearranging terms,

P(B − A) = P(B) − P(A)

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2021-12-05 00:00
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