Addendum
Here's how the probabilities in the Table posted above were calculated. Take, for example, the probability of having 6 outs and hitting 1 or 2 outs on the Turn and the River.
C(6,2)=15 is the number of 2-card combinations that those 6 outs can produce. That means there are 15 combinations of Turn+River whereby you hit your outs in both cards.
For the number of hitting only 1 out (and get 1 blank), you have 6 outs and (52 - 2cards in your hand - 3cards on the flop -6 outs)= 41 blanks. Combining the outs with the blanks gives you 6*41=246 combinations whereby you hit only 1 out on Turn+River.
So, we have 15+246=261 combinations producing either 1 or 2 outs on Turn+River.
The total combinations of all the remaining cards that can be seen on Turn+River are
C(47,2)=1081.
Therefore, the probability of getting a combination of Turn+River that hits you with 1 or 2 outs is 261/1081=0.241443108233117483811285846438483 or 24.1%.
[It is irrelevant in this calculation whether you hit your 1 out on the Turn or on the River. The probability of hitting 1 out in either Turn or River is the same, before the Turn card is dealt.]
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