(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

[itex]A \setminus B[/itex] denotes set difference; these are probability functions.

3. 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!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Probability P(A\B) = P(A) - P(B)

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