I am looking for a formula that will help in Texas Hold'em poker.
Essentially I am looking for formula that will tell me the chance of
an event happening if there are two chances that it can occur.
Example: if there are two cards to come (ie the turn and the river),
what are the chances that one of those cards will give me a flush
(assuming I have 4 to the flush already)? A formula and not a strict
answer to the above question would be helpful so that I can use the
formula in other situations. Thanks a lot!

The formula is derived from the odds of each card being what you want:

(I'll assume you want a flush in clubs because that is the best suit ever!)
For the first card, you know 5 of the 52 cards in the deck are.  So
there are 47 unknown cards... and for your flush you know that 4 of
the 13 possible clubs are already in your sight.  So ther are 9 clubs
remaining.  9/47 = 19.1%
If you haven't gotten your flush yet, then you know 6 of the 52
cards... and you know that 4 of them are clubs.  The odds this time
are 9/46 = 19.6%.

We can't just add 19.1% + 19.6% because that would double count any
instance when both cards would be clubs.  So instead it is 19.1% +
19.6% - (19.1%*19.6%) = 35%.

Sorry there isn't a more clear cut formula.  But I hope I left a good
enough reasoning trail that you can derive formulas for other
instances you need.  Just look at what cards you know and what cards
you need... then the math usually falls in line without too much
struggling.

Something that many people don't learn very quickly in holdem is that
... when trying to get a flush by paying to see the turn card, you
then usually have to pay for the river card as well.  So in essence
whatever you pay for the turn card only gives you a 19.1%, and then
you have to pay again (usually more) to see the river card for that
19.6% chance of getting the flush.  (unless of course you go all in
after the flop)

A less accurate but easier to calculate formula is to multiply the
number of outs by four to get the percentage chance of making your
hand with two cards to come, or multiply by two to get the percentage
chance of making your hand with one card.

http://casinogambling.about.com/library/weekly/aa050103.htm

hey thanks a lot, that definitely helps..