math help

[Kuciwalker]

Let (A,B) be independent events. Show that (A,Bcomplement) and (Acomplement,Bcomplement) are independent.

Um, A and B are independent if they're disjoint, right? So wouldn't Bc contain A and therefore not be independent of it?

[KrazyHorse]

Um, A and B are independent if they're disjoint, right?

Errr....no

[Kuciwalker]

Thank you.

[KrazyHorse]

Proof is as follows:

Pr(A) = Pr(B)*Pr(A|B) + Pr(Bcomplement)*Pr(A|Bcomplement)
Pr(Bcomplement) = 1-Pr(B)
=>Pr(A) = Pr(B)*Pr(A|B) + (1-Pr(B))*Pr(A|Bcomplement)
Pr(A) = Pr(A|B) (defn of independence)
=>Pr(A) = Pr(B)*Pr(A) + (1-Pr(B))*Pr(A|Bcomplement)
=>(1-Pr(B))*Pr(A) = (1-Pr(B))*Pr(A|Bcomplement)
If Pr(B) = 1 (or 0) then statistical independence is meaningless, so:
=>Pr(A) = Pr(A|Bcomplement)

QED

The second part is obvious once this is proven

[Asher]

What he said. And like, stuff.

[KrazyHorse]

Hmm. Defn actually goes by Pr(A && B) = Pr(A)*Pr(B), so better proof is (quite similar though)

Pr(A) = Pr(A && B) + Pr(A && Bc)
Pr(A) = Pr(A)*Pr(B) + Pr(A && Bc)
Pr(A) * (1 - Pr(B)) = Pr(A && Bc)
Pr(A) * Pr(Bc) = Pr(A && Bc)

QED

[Asher]

wuat ab08t tue s0c90p0g9cap

ack, key shift

What about the sociological aspects?

[Wiglaf]

math

[Barnabas]

whats the meaning of qed?

[RGBVideo]

Quod era demonstrandum, Latin for "which was demonstrated". QED is written after you've proven something with mathematical terms.

[KrazyHorse]

actually, it's "which was to be demonstrated"

[KrazyHorse]

and it's quod erat demonstrandum

[Barnabas]

No that different from spanish, I recongnize the 3 words, I wonder if latin isnt that difficult for a spanish speaker

[Fake Boris]

vj is so brilliant

[OzzyKP]

Since the problem is way over my head and resolved, allow me to make a multi-purpose math threadjack.

I'm tutoring this guy, a 9th grader, and he is really struggling with math (and most other subjects), but the math is what gets to me most. He is doing simple algebra stuff, solving for x, and it is just not sinking in at all. He is frustrated and I feel helpless.

It is all very abstract to him and he just isn't getting the logic behind math.

I'll try to explain later when I'm less sleepy/sunburned. But if anyone has ideas for explaining things to him better, I'm all ears.