- #1
magicarpet512
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Homework Statement
Let [itex]A \subseteq B \subseteq S[/itex] where [itex]S[/itex] is a sample space.
Show that [itex]P(A \setminus B) = P(A) - P(B)[/itex]
Homework Equations
[itex]A \setminus B[/itex] denotes set difference; these are probability functions.
The Attempt at a Solution
I have,
[itex]P(A \setminus B) = P(A \cap B^{C})
= P(A) - P(A \cap B)
= P(A) - [P(B) - P(A^{c} \cap B)]
= P(A) - P(B) + P(A^{c} \cap B)[/itex]
It seems like I'm close, but I've spent a while trying to figure out how to get rid of the [itex]P(A^{c} \cap B)[/itex].
Any insight anyone?
Thanks!