Conditional Probability

[akk]

Let me preface this post by saying that I've never formally learned any prob or stat. Everything I know is from life experience and an Actex manual.

Anyhow, here's my question: does P[A union B | C] = P[A|C] + P[B|C] - P[A intersection B | C]. It certainly seems like it would be but I can't fully convince myself.

Also, if you know of a proof of this equality please share!

[abacustwo]

Just use the definition of conditional probability.

P[A U B|C] = P[(AUB) intersection (C)]/P[C]
= P[(A intersection C)U(B intersection C)]/P[C]
= P[A intersection C]/P[C] + P[B intersection C]/P[C] - P[A intersection B intersection C]/P[C]
= P[A|C] + P[B|C] - P[A intersection B|C]

[akk]

Just use the definition of conditional probability.

P[A U B|C] = P[(AUB) intersection (C)]/P[C]
= P[(A intersection C)U(B intersection C)]/P[C]
= P[A intersection C]/P[C] + P[B intersection C]/P[C] - P[A intersection B intersection C]/P[C]
= P[A|C] + P[B|C] - P[A intersection B|C]

Thanks!