SOLUTION: What are the odds of getting the same cards (2) twice from a shuffled deck?

Question 556182: What are the odds of getting the same cards (2) twice from a shuffled deck?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you draw a card from the deck.
it can be any card so the probability of getting any card is 52/52 = 1.
now you put that card back in the deck and draw again.
the probability you will get that same card again is 1/52.
the combined probability is 1/1 * 1/52 = 1/52.
the odds of getting that card again is the probability of getting that card again divided by the probability of not getting that card again.
since the probability of getting that card again is 1/52, then the probability of not getting that card again is 1 - 1/52 = 51/52.
the odds of getting that card again is therefore equal to:
1/52 / 51/52 = 1/52 * 52/51 = 1/51.

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