Re: Odds of getting a pair on the flop?
No you don't add probabilities for events occuring in sequence. Why? Say you wanted the total probability of tossing at least one head in two coing tosses. Using your approach it would be 0.5+0.5 = 1 (ie it must certainly happen) - not correct. You multiply the probability the thing won't happen at each step, and then multiply the results and subtract from one(for the coin toss = 1-(0.5*0.5) == 0.75 or 75% chance a head will occur at least once in 2 coin tosses)
so for your question:
You work out the odds of not pairing at each turn, and multiply them, and then subtract from 1 (the sum of all probabilities)
44/50 * 43/49 * 42/48 = 0.67 (67%)
This is the probability you won't pair, so by definition the chance you pair with either of your hold cards is:
1-0.67 = 33%
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