Looking for a hint on a stats proof

[bennyska]

so I'm somewhat new to statistics proofs, but this one is for the most part a sets proof, which i can do. I'm having trouble connecting them.
(c = complement)(AB = A intersect B)

Let A_1, A_2... be any infinite sequence of events, and let B_1, B_2... be another infinite sequence defined as B_1=A_1, B_2=A_1cA_2, B_3=A_1cA_2cA_3 and so on.
Prove that Pr(Union i=1 to n A_i) = Sum i=1 to n Pr(B_i).
(sorry if that notation is hard to understand)

So I've convinced myself that this is true. I see if i take the union of A_i up to n, that B_i up to n is equal. Each B_i is A_i minus any previous As that intersect it. I'm just having trouble saying that in math. If I had to write a proof right now, I'd say each Sum B_i = Union A_i, so they're equal.

So yeah, if i could get some hints on where to start. Thanks.

 

[EnumaElish]

What does "Sum B_i" mean? Can you add sets?

I would have defined Z_k = union of A_i up to k.

Show the equality holds for k=1, and it also holds for k+1 assuming it does for k.

 

[bennyska]

i have since restarted this thread over in the homework section. i do have a proof there, if you wouldn't mind taking a peek at it, see if it looks okay. the thread has the same name as this one.