if I were to pick a card from a standard deck, shuffle and do it 9 more times, what is my probability that at least 2 of the 10 cards I draw are the same?

If you have a standard deck, you shouldn't have ANY of the same card.

If you DO---someone's been cheating at poker.

Assuming that the cards are replaced after each draw, the second draw would have a 1 in 52 chance of being the same card as the first draw. The third draw would have a 2 in 52 chance of being the same as either of the first two draws. The fourth draw a 3 in 52 chance of matching the first 3 draws... the tenth draw a 9 of 52 chance of being the same as the previous 9 draws. All of these probabilities are independent and thus cumulative so, the probability would be (9+8+7+6+5+4+3+2+1)/52 or 45/52. Quite likely!