I\'m in need of some help on how to get started. I\'d rather not havethe whole a

Question

I'm in need of some help on how to get started. I'd rather not havethe whole answer given to me, but if that's required then that'sokay too.
If you have 2 decks of cards, and you flip one card from bothdecks over, you have a 1/52 chance of the card from the second deckmatching the one from the first deck, and vice versa. What I want to do is figure out the chances of not getting asingle match from either deck, and then taking 1 and subtractingthe number from it to find my chance of getting at least 1match.
So what you would start with is a 51/52 chance of not gettinga match after a card from the first deck has been drawn. After this, I am a bit lost because after you draw a secondcard from the first deck, you have a 50/51 chance that the cardfrom the first pile will match the card from the second pile, butthis isn't really true because the second deck has a "dead" cardthat matches the first card that you drew from the firstdeck. I'm not sure how to account for this, as 49/51 seems too easyto be true. Edit: Well, I'm sure the 49/51 was too good to be true, butnow my problem is that I noticed, what if the card that you get ridof in the first pairing is the card that would match in the secondpairing? Then there would be a 100% chance that you wouldn't get amatch because the card doesn't exist in the pile anymore.
I'll keep trying! Thank you anyone who helps.
I don't actually need this by any date, this is a personalproblem not a school problem, but it would be nice to get itsoon-ish. Thanks you!
If you have 2 decks of cards, and you flip one card from bothdecks over, you have a 1/52 chance of the card from the second deckmatching the one from the first deck, and vice versa. What I want to do is figure out the chances of not getting asingle match from either deck, and then taking 1 and subtractingthe number from it to find my chance of getting at least 1match.
So what you would start with is a 51/52 chance of not gettinga match after a card from the first deck has been drawn. After this, I am a bit lost because after you draw a secondcard from the first deck, you have a 50/51 chance that the cardfrom the first pile will match the card from the second pile, butthis isn't really true because the second deck has a "dead" cardthat matches the first card that you drew from the firstdeck. I'm not sure how to account for this, as 49/51 seems too easyto be true. Edit: Well, I'm sure the 49/51 was too good to be true, butnow my problem is that I noticed, what if the card that you get ridof in the first pairing is the card that would match in the secondpairing? Then there would be a 100% chance that you wouldn't get amatch because the card doesn't exist in the pile anymore.
If you have 2 decks of cards, and you flip one card from bothdecks over, you have a 1/52 chance of the card from the second deckmatching the one from the first deck, and vice versa. What I want to do is figure out the chances of not getting asingle match from either deck, and then taking 1 and subtractingthe number from it to find my chance of getting at least 1match.
So what you would start with is a 51/52 chance of not gettinga match after a card from the first deck has been drawn. After this, I am a bit lost because after you draw a secondcard from the first deck, you have a 50/51 chance that the cardfrom the first pile will match the card from the second pile, butthis isn't really true because the second deck has a "dead" cardthat matches the first card that you drew from the firstdeck. I'm not sure how to account for this, as 49/51 seems too easyto be true. Edit: Well, I'm sure the 49/51 was too good to be true, butnow my problem is that I noticed, what if the card that you get ridof in the first pairing is the card that would match in the secondpairing? Then there would be a 100% chance that you wouldn't get amatch because the card doesn't exist in the pile anymore.
I'll keep trying! Thank you anyone who helps.
I don't actually need this by any date, this is a personalproblem not a school problem, but it would be nice to get itsoon-ish. Thanks you!

Explanation / Answer

I'm trying to figure out the chances of taking two decks, thenflipping the top card and seeing if it matches, then the secondcards in each deck and seeing if those match, then the third, etc.all the way to flipping the last card and seeing if thosematch.

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