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Discussion in 'The Front Room' started by kirennia, Jun 10, 2007.

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  1. Moriath

    Moriath I am a FH squatter FH Subscriber

  2. Lamp

    Lamp I am a FH squatter

    Here's one for you.

    5 people each have a standard deck of 52 cards. They each shuffle their pack randomly. Each person draws one card, places it face down, and after everyone has a card, they all turn them over.

    What is the probability that everyone has the same card?

    (eg 5 x 6 of clubs; 5x jack of spades, etc)
     
  3. Scouse

    Scouse HERO! FH Subscriber

    One in 380,204,032?
     
  4. Wij

    Wij I am a FH squatter FH Subscriber

    52 times too high:

    7,311,616
     
  5. Rubber Bullets

    Rubber Bullets Resident Freddy

    Why is that Wij? I got the same as Scouse, 52^5 is that wrong?
     
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  6. Moriath

    Moriath I am a FH squatter FH Subscriber

    Maybe the first guy doesnt have to match with anyone so his draw could be any card? Its the only reason i could think of to not x the last 52
     
  7. Moriath

    Moriath I am a FH squatter FH Subscriber

  8. Lamp

    Lamp I am a FH squatter

    All 5 cards have to match. The order is irrelevant
     
  9. caLLous

    caLLous I am a FH squatter

    Without putting too much thought into it, I'd say 52 ^ <number of packs> as well. If there were only 2 packs there wouldn't be 52 possibilities, there'd be 52^2.
     
  10. Rubber Bullets

    Rubber Bullets Resident Freddy

    Yeah, that's it isn't it. The first guy picks any card, so the second guy has a 1 in 52 chance to match it. The third guy 1 in 52^2, and so the 5th 1 in 52^4.
     
  11. Lamp

    Lamp I am a FH squatter

    I got what @Wij had. It was a question on QI (series M).

    (1/52)^4

    but according to the "QI elves" the odds are one in 2 billion. Eh?

    I'll ask my sister. She has a degree in mathematics.
     
  12. Job

    Job The Carl Pilkington of Freddyshouse

    Thats where probability blows my skull.
    If its 1/52 say to get the 5 clubs..then the next day I say whats the prob of the 5 of clubs, its the same 1/52.
    But I got a 5 clubs yesterday...doesnt matter
    But if I turned two seperate packs at the same time it wouldnt be 1/52 for them both being 5 clubs.
    That would be joint probability
    How small a time gap can you leave..how does this work?

    What's the Difference Between Probability and Cumulative Probability?
     
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  13. caLLous

    caLLous I am a FH squatter

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  14. Scouse

    Scouse HERO! FH Subscriber

    That's horrid.

    Not to belittle in any way - it's interesting to make the point that we were at over 8 times that (at 854) on daily deaths from coronavirus.
     
  15. Zarjazz

    Zarjazz Unemployed Bum Travelling The World.

    Because while 52^5 is the odds of one particular identical combination (say all Ace of Spades), since there are 52 possible combinations where all cards match the odds are then 52^5 / 52 = 52^4.

    I'm almost certain the QI Elves are wrong about this one unless there was some other detail in the original question that changes the described scenario.
     
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  16. Scouse

    Scouse HERO! FH Subscriber

    I don't follow that. Pls explain.

    If one card combo is 52^5 the existence of other combos is independent and the chances of one of those other combos is the same, independent, probability. No?
     
  17. caLLous

    caLLous I am a FH squatter

    Because if you have 2 packs of cards and you pick one card from the first pack, there's a 1 in 52 chance that you pick the same card from the second pack, so it's 52 ^ <number of packs - 1>.
     
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  18. Scouse

    Scouse HERO! FH Subscriber

    That's unrelated to @Zarjazz' explanation which is about cards, not packs?

    Anyway, because the draws are unrelated to each other the probability should be calculated multiplicatively like this:

    1/52 x 1/52 - for 5 packs.

    The draw of a card from any pack has no effect on any subsequent draws.
     
  19. Scouse

    Scouse HERO! FH Subscriber

    It's been a while since I had to look up basic rules of probability. But here goes.

    The pertinent bit:
    So, multiply the probabilities of separate independent events.

    Edit. Gah, barely readable, but that's what it says :(
     
  20. Scouse

    Scouse HERO! FH Subscriber

    I do get your point about packs. But yoir thinking seems to imply conditionality.

    Think of it as either one pack of cards with the selected card being replaced and the cards shuffled, or, five packs of cards all having a card picked at the same time - each deck has a probability of 1/52 for a specific card, independently...
     
  21. Wij

    Wij I am a FH squatter FH Subscriber

    The chance of drawing the 'right' card from the first deck is 1. It's then multiplied by 52 for each of the subsequent decks.

    Shall we do the Monty Hall problem next?
     
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  22. Job

    Job The Carl Pilkington of Freddyshouse

    The universe isnt interested in our attatchment to individual cards.

    Thats what starts to eat in to me, Im sure the key to consciousness is hidden in probability.
     
  23. Job

    Job The Carl Pilkington of Freddyshouse

    Celebrity deaths.
     
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  24. Zarjazz

    Zarjazz Unemployed Bum Travelling The World.

    We are furiously agreeing. I just flipped the odds so it may look confusing. 52 x probability of each unique combination (1 / 52^5)
     
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  25. Scouse

    Scouse HERO! FH Subscriber

    My favourite type of agreeing :)

    In fact my favourite type of a lot of things you do in front of the internet :oops:
     
  26. Scouse

    Scouse HERO! FH Subscriber

    Nope. It's 1 in 52. :)

    You're creating conditionality (bad english I know) if your looking at it after you've drawn your first card - but we're looking at five untouched decks and saying "what's the chance of drawing five the same?"

    Five blokes, 3... 2... 1... draw! :)
     
    Last edited: May 23, 2020
  27. Rubber Bullets

    Rubber Bullets Resident Freddy

    1 in 52 is the chance of drawing a specific card from the first deck. In this case we don't care what that card is, so the first deck just acts as a random card generator, the only requirement is that the card from the second deck needs to match it, with the odds of 1 in 52. for the third deck then to match is 1 in 52^2 etc.

    I've no idea what you mean by conditionality in this case, but I don't think it's relevant, all three cards can be drawn at the same time or in order, the odds don't change.

    And I don't care what anyone else says, the fucking plane will take off!! :mad:
     
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  28. Wij

    Wij I am a FH squatter FH Subscriber

    I’m right.
     
  29. Zarjazz

    Zarjazz Unemployed Bum Travelling The World.

    You are but what were the odds of that ...
     
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  30. Wij

    Wij I am a FH squatter FH Subscriber

    Correct on both.
     

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