Probability questions?

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  • Brio said:
    Are the cards shuffled between draws?
    I do not see how that would make a difference as it would not affect the ratio of cards, and also they are in a bag.

    @Brio, how does this influence probability?
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  • HAL9000 said:
    1 in 4 for the first attempt, then 1 in 3 for the second. Add them together = 7 in 12 or 0.58333...
    (I think)
    Despite having two attempts from four cards I don’t think the answer is 50%. This is because the first-picked card doesn’t go back into the bag thus giving the second attempt (if required) better odds.
    Ask yourself what your answer would be if the player got to go for a third attempt. 
    So 7/12ths plus 6/12th which is 13/12. And obviously wrong. 

    Interesting as I’d got 7/12 as well. 

    Not winning as per Musicwolf is 3/4 x 2/3 = 6/12. Which seems to be the correct answer although I’m not entirely sure I understand why. 
    On the occasions where the player wins on the first attempt, they don't then draw a second card, so the opportunity to get a 1/3 win doesn't exist. This, along with the fact that extending to a third attempt is obviously wrong, should convince you that you can't just add the probabilities together - the events aren't truly independent. 

    The answer to these questions is almost always to consider the odds of not winning and then invert it at the end. It's normally much easier both conceptually and mathematically. 


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  • bertiebertie Frets: 13564
    bertie said:
    Philly_Q said:
    I've got a degree in Statistics but I honestly can't remember any of it.
    I was 50% sure you'd say that
    I was 50% sure that @Philly_Q would say that, and if that were to occur,  50% sure that you'd say that in reply. This which means that I sure there was a 25% chance of you saying that.
    are you sure ?
    just because you don't, doesn't mean you can't
     just because you do, doesn't mean you should.
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  • bertie said:
    bertie said:
    Philly_Q said:
    I've got a degree in Statistics but I honestly can't remember any of it.
    I was 50% sure you'd say that
    I was 50% sure that @Philly_Q would say that, and if that were to occur,  50% sure that you'd say that in reply. This which means that I sure there was a 25% chance of you saying that.
    are you sure ?
    Kinda :P 
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  • bertiebertie Frets: 13564
    thats definite then 
    just because you don't, doesn't mean you can't
     just because you do, doesn't mean you should.
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  • fretmeisterfretmeister Frets: 23906
    Brio said:
    Are the cards shuffled between draws?
    I hope so. That makes it far easier to stop him getting the right one.

    He might even notice by the 10th card.



    Strangefan
    said:
    Speaking as a magician.

    If the bag belongs to me, then you'll get the right card when I am damn well ready for you to have it!
    Now that's a skill, the hand and misdirection skills  you guys have is amazing, I have a small hobby of workng out magic tricks, the psychology part of it always intregues me. 
    @Strangefan ;

    Treat yourself to this 

    https://www.amazon.co.uk/gp/product/1523507438/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

    It's not a "how to do it" book - it's all about the thought process. Joshua Jay is one of my favourite magicians, and he writes in a very easy style, a long way away from the old top hat and dove tropes.
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  • MusicwolfMusicwolf Frets: 3627
    bertie said:
    bertie said:
    Philly_Q said:
    I've got a degree in Statistics but I honestly can't remember any of it.
    I was 50% sure you'd say that
    I was 50% sure that @Philly_Q would say that, and if that were to occur,  50% sure that you'd say that in reply. This which means that I sure there was a 25% chance of you saying that.
    are you sure ?
    Kinda :P 
    My degree is in Physics.  We can exist in both states, sure and unsure, simultaneously as long as nobody tries to measure us or unless we don't like cats.

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  • stickyfiddlestickyfiddle Frets: 26743

    @Strangefan ;

    Treat yourself to this 

    https://www.amazon.co.uk/gp/product/1523507438/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

    It's not a "how to do it" book - it's all about the thought process. Joshua Jay is one of my favourite magicians, and he writes in a very easy style, a long way away from the old top hat and dove tropes.
    My understanding, as a layperson, is that magicians are just colossal bullshitters who have no problem talking nothing but lies to people they've never even met before. It's actually quite impressive!
    The Assumptions - UAE party band for all your rock & soul desires
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  • AdeyAdey Frets: 2208
    edited January 2022
    I'm with @Philly_Q - If only I could remember my O & A level maths and Statistics...
    nPr  or nCr would do it I recall. P is permutations where cards aren't replaced and C is Combinations where they are.

     It'll be something involving the likes of n!/(n-r)!r! Or something like that?
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  • fretmeisterfretmeister Frets: 23906

    @Strangefan ;

    Treat yourself to this 

    https://www.amazon.co.uk/gp/product/1523507438/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

    It's not a "how to do it" book - it's all about the thought process. Joshua Jay is one of my favourite magicians, and he writes in a very easy style, a long way away from the old top hat and dove tropes.
    My understanding, as a layperson, is that magicians are just colossal bullshitters who have no problem talking nothing but lies to people they've never even met before. It's actually quite impressive!
    Yeah - but we are honest about it!

    Magicians are honest liars.

    Mediums are just dishonest magicians.
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  • Philly_QPhilly_Q Frets: 22515
    edited January 2022
    Adey said:
    I'm with @Philly_Q - If only I could remember my O & A level maths and Statistics...
    nPr  or nCr would do it I recall. P is permutations where cards aren't replaced and C is Combinations where they aren't.

     It'll be something involving the likes of n!/(n-r)!r! Or something like that?
    Blimey @Adey, that's more than I can remember, well done!

    The thing I've found whenever somebody raises a question about statistics and probability, there's no point almost remembering the theory, it's completely useless unless I'm absolutely sure what I'm talking about.  And I'm not!
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  • StrangefanStrangefan Frets: 5845
    Brio said:
    Are the cards shuffled between draws?
    I hope so. That makes it far easier to stop him getting the right one.

    He might even notice by the 10th card.



    Strangefan
    said:
    Speaking as a magician.

    If the bag belongs to me, then you'll get the right card when I am damn well ready for you to have it!
    Now that's a skill, the hand and misdirection skills  you guys have is amazing, I have a small hobby of workng out magic tricks, the psychology part of it always intregues me. 
    @Strangefan ;

    Treat yourself to this 

    https://www.amazon.co.uk/gp/product/1523507438/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

    It's not a "how to do it" book - it's all about the thought process. Joshua Jay is one of my favourite magicians, and he writes in a very easy style, a long way away from the old top hat and dove tropes.
    It's in the basket, thank you 
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