probability of top pair on flop

[tommo]

What is the probability that a non pair hand makes top pair or better on the flop?

specifically I'm interested in hands like:
KQo
AKs
A2
A2s
AQo

This shouldn't be too hard to do...I'm just having a brain fart. Thanks in advance.

[Galois]

For KQ the calculation goes like this: For the flop there are 50 choose 3 combinations of flops. I'll write this as C(50,3).
This is your denominator because it represents your sample space.
For the numerator we have 3 kings and we need one this is
C(3,1)=3 times C(43,2). This is why you get C(43,2)
There are now 49 cards left in the deck (after your pocket cards and the king on the flop) minus the 4 aces (we don't want over cards) minus the two other kings ( we don't want trips). That leaves us with 43 cards and we need to choose 2 of them. So finally it is
3*C(43,2)/C(50,3) = 0.1382.
Note that this calculation does not exclude you flopping top two pair. Hopefully this helps you figure out the probability of the rest of hands you are interested in.