Exercise 1.44

Question

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 $A \subseteq B$, then
$$
P(B-A)=P(B)-P(A)
$$
directly using the axioms of probability.

fifthist x · Accepted Answer

Since $B = (B-A) \cup A$, $P(B) = P(A) + P(B - A)$ by the second axiom of
 probability. Rearranging terms,
$$P(B-A) = P(B) - P(A)$$

Exercise 1.44

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Exercise 1.44

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