[scottjack]

perhaps I'm missing something as well, but wouldn't the probability of x, the card that doesn't match either of your hole cards be 44/50, not 48/50 ?
there are 3 remaining a's and 3 remaining b's in the deck. subtracting these 6 from the 50 cards remaining leaves 44.

Also, while it's true that the probability of two or more events occurring at the same is found by multiplying the individual event probabilities, this is only so when the events are independent . i don't think this would apply here.

For instance, the probability that the 3rd 'a' falls, IS affected by the fact that the 2nd has already fallen.

As an example, (assuming neither of the hole cards is a 7)the probability that the event of "first flop card is a 7" is 4/50. if the event "second flop card is a 7" were independent of the first, then its probability would also be 4/50 and the probability of both events occurring would be (4/50)^2 however, the probability of these 2 both occurring is (4/50)*(3/49).

i think this may get messy, but there's going to have to be some conditional probabilities figured into things before it's all said and done.


I'm sure i could very well be wrong on all of the above. Just thought i might shed some light on your quandary.

Hope this helps a little.