Hi VJesus12,
With a standard 52-card deck, each 'value' appears 4 times (four kings, four 10s, four 3s, etc.). The probability of getting a matching pair (meaning ANY pair) is different from the probability of getting a specific pair (for example, two kings). Both of those probabilities appear in the answer choices though, so you have to be careful with these types of questions - make sure that you answer the question that is ASKED.
Since we're looking for the probability of pulling ANY matching pair - and each value appears 4 times - there's an equal probability that the first card will be any of the 13 possibilities. Thus, the first card doesn't really matter - it's the SECOND card that matters (since we need it to match the first). Once that first card is drawn, there are only 3 more cards in the deck (out of 51 remaining cards) that would match the first card. Thus, the probability is 3/51 = 1/17.
Final Answer: C
As an aside, the probability of pulling a SPECIFIC pair (for example, two kings) requires that BOTH cards match the specific value that you're looking for:
For the 1st card, there is a 4/52 probability of drawing that card. Assuming that 1st card matches....
For the 2nd card, there is a 3/51 probability of drawing that card.
Thus, the probability would be (4/52)(3/51) = 12/2652.... but that is the answer to a DIFFERENT question.
GMAT assassins aren't born, they're made,
Rich
