Based on Wikipedia article, probability of making two pairs among seven cards is 23.5%. But this include cases where the two pairs are on the board (e.x. I have AQ and the board is KKJJ5), or one of the pairs is on the boards and the other pair is with one of the cards I have in my hand (e.x. I have AQ and the board is KKQ53). I want to know the probability of making two pairs using only the (unpaired) cards that I have in my hand. For example I have KJ, and the boards is J92K7. In other words if I have two unpaired cards, what are the chances that both of my cards get paired with the board?
I take it that you are not seeking exactly two-pair probability, but rather "hitting with both cards once each".
In such case, 5 cards of the board must contain two of your cards and any of three other cards.
P = C(3,1)×C(3,1)×C(44,3)
C stands for "Combin".You divide that result by C(50,5) and thats your answer.
Please note, the above calculation will include the boards like KJ222, which overrides your two pair, but I guessed thats what you were asking for.