Probability Question?

It means 'on average' if you kept dealing over and over again, that you would get about 1 hand with 2 pairs every 21 times.

If you dealt 1,000,000 hands, on average you would get about 47,619 or two pairs roughly once every 21 hands. You may get more, you may get less, but the more hands you deal, the more likely you will end up with about 4.76% of the hands being 2 pairs.

The reason that it does not guarantee you a two-paired hand every 21 times is that usually hands are shuffled after each deal so each deal is a new event. The cards have no memory of what they just did. Therefore you could have 21 straight hands of two pairs, or you could have 1,000 straight hands without two pairs, but on average over an incredibly long period of time, your average will move closer to 4.76%

1/21 means that if you were dealt 21 hands of 5 card poker you would get 2 pairs 1 time

It means that if you were to deal 21 five-card hands, 1 of those hands would have two pairs in it.

More accurate solution:

Total: 52C5

Two pairs: 13C2(4C2)^2(48)

p = 13C2(4C2)^2(48)/52C5 = 216/4165, which means that if you deal 4165 hands of 5 cards, you most likely to get 216 two pairs.

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You cannot say "exactly" about probability.