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I know the probability of getting a pocket pair is 5.88%. I know the probability of then getting the 3 card on the flop is 10.78% (removing possiblity of full house and 4K).

So is the total possibility of getting 3K, before any card is dealt, 10.78% - 5.88% = 4.89?

In short my question is, if you have 52 cards, what is the probability of dealing two cards that match and then collecting the third card when the next three cards are dealt?

Thank you

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No, you need to multiply the probabilities. Assuming your numbers are correct, it would be P(flopped set) = P(pocket pair) * P(flop the third)

P = 0.0588 * 0.1078 = .0063

So without other knowledge, the chance of getting a flopped set on any deal is a bit better than 1/2 of 1%.

Another way to look at this is that the pocket pairs should arrive about once every 17 hands. Then with pocket pairs you flop the set 1 out of 9 hands. So a flopped set 1 out of 9*17 or a bit more than 1 out 160 hands.

And that's the probability of 3K on the flop.

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