Questions Re: Outs/Probability/Percent Chance

[Civiliste]

X-posted: Beginners' Questions

Okay, I have a reallllly n00b question about calculating percent chance to catch:

#1.) One of my outs on the Turn (calculation at the Flop)
#2.) One of my outs on the River (calculation at the Turn)
#3.) One of my outs on either the Turn or the River (calculation at the Flop)

What are the correct formulae for these calculations?

Am I correct that:

Given:
X = number of (clean) outs
Y = probability (%) of hitting an out

Is the formula for:
#1: Y = (X/47)*100
#2: Y = (X/46)*100
#3: Y = ((X/47) + ((47-X)/47)*(X/46))*100

Given the preceding equations, I arrive at the conclusion that:

Given 11 outs at the Flop:

Is it correct that:
Percent Chance to catch on the Turn: 23.4%
Percent Chance to catch on the Turn or River: 41.72%
Probability to catch on the Turn: 1147-11) = 1:3.27
Probability to catch on the Turn or River: (Need a formula for this)

Secondly, how do you discount possibly tainted outs? If I have a read on opponent, or a suspicion that an out is tainted that equates to a 40% confidence, should I:

#1. Discount the tainted outs by .4
#2. Not discount the tainted outs at all
#3. Discount the tainted outs to 0
#4. Discount the tainted outs to 0 if confidence > 50%, do not discount the tainted outs at all if confidence < 50%

It seems that #1 would be the mathematically correct approach, but that #2 would result in a looser approach, #3 might result in playing too tight, and #4 would be baloney [sic], but would impart to my game at least a minimal measure of the appearance of randomizing play styles. What approach is recommended?

Am I calculating correctly? I really want to get the formulae down cold before I proceed with my game. I have a degree in Economics, but it's been 3 years since Econometrics, and 7 years since STAT 214, so I can't remember formulae to save my life!

Thanks for any help,
-Zak