I want to know the probability of getting a pair after all 5 cards are dealt on the table and assuming that I haven't got a pocket pair.
Let's assume that I hold an ace and a king and 50 cards are left. So the probability of getting a pair is: P(getting an ace) + P(getting a king) + P(5 table cards having a pair of anything else than ace or king)
Then:
$P(pair) = \frac {3}{50} + \frac{3}{50} + \frac{44 \times 3 \times 40 \times 36 \times 32 \times {5 \choose 2}}{50 \times 49 \times 48 \times 47 \times 46} = 0.3592 = 35.92\%$
Am I thinking correct?