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Thread: Let's pick a tungsten point...

  1. #1
    digitus impudicus
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    Let's pick a tungsten point...

    Suppose you're shooting with a famous archer at his range at home.
    You both start shooting and all of a sudden, he says "Damn!" and stops.
    You ask what's up and he pulls out all his arrows and holds them up.

    All but two have tungsten points.

    You offer to go get two more to make a full set and walk into his shed.

    He calls out to you:
    "I was refletching yesterday.
    There should be a mix.
    There are three arrow tubes.
    One will have two tungsten arrows.
    One will have two stainless
    and the other will have a stainless and a tungsten point."

    No problem.
    You walk up to the closest arrow tube and pull an arrow out. It's a tungsten point.

    What are the chances that the remaining arrow in the tube is also a tungsten point?
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  2. #2
    Learning the Ropes
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    Learning the Ropes
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    1/3

  4. #4
    digitus impudicus
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    Anyone else?
    Status is not defined by the amount of gear in your signature.
    Performance cannot be purchased.

    "The Internet offers everything - except quality control" - K. Anders Ericsson.


  5. #5
    2nd Class sb954's Avatar
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    Sent from my SM-N910G using Tapatalk

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    3rd Class whoknows's Avatar
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    Thanks Andy, my head hurts now after reading that

  7. Thanks Andy! thanked for this post
  8. #7
    digitus impudicus
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    Quote Originally Posted by sb954 View Post
    100%
    100% ? But there's one tube that has a tungsten and a stainless in it. What's to say you haven't gone to that tube, and pulled the tungsten out first? That would be zero percent if you were at that tube.
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  9. #8
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    Quote Originally Posted by iandall View Post
    1/3
    Actually, I take it back. Phil is right. 50%.

    Somehow I jumped to the conclusion that there were two mixed tubes. I guess I was still thinking about two-up.

  10. #9
    digitus impudicus
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    This probability question is well over a century old.

    Nobody here has posted the correct answer yet.
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  11. #10
    1st Class Matrix Makeover's Avatar
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    Quote Originally Posted by Andy! View Post
    This probability question is well over a century old.
    Is it the expensive version of the socks in the drawer scenario? I can't be bothered, but if that is the right comparison, it might help someone else?
    "I used to read, but it's faster to make up stuff" - Wally (Dilbert)

  12. #11
    digitus impudicus
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    No.
    Status is not defined by the amount of gear in your signature.
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  13. #12
    Learning the Ropes
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    33.33333333333333333333333333333333333333333333333 33333333333333333333333333333333333333333333333333 33333333333333333333333333333333333333333333333333 333333333333333333333333333333333333%

  14. #13
    1st Class Matrix Makeover's Avatar
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    Quote Originally Posted by Andy! View Post
    No.
    Then I'll pretend to be clumsy so they think it better that they get their own arrows themselves
    "I used to read, but it's faster to make up stuff" - Wally (Dilbert)

  15. #14
    digitus impudicus
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    Still no correct answers yet.

    Hints:

    This question is designed so that you look at it incorrectly and will intuitively get wrong.

    I would suggest looking at the layout visually. Draw the options. Then look at the single part of the question that refers to the odds or likelyhood of the second arrow having a tungsten point.

    That should rearrange how you percieve the issue. It has three parts, not two.
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  16. #15
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    66.66% recurring
    Last edited by DaddyDugong; 5 Days Ago at 12:10 PM.

  17. #16
    Master Bowman Bottom Dweller's Avatar
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    Archery's a lot like Life .... a few see it as an opportunity to score cheap points; while the rest are focused on the ends that count.
    Genesis 21:20 And God was with the boy as he grew up in the wilderness. He became a skillful archer.

  18. #17
    Master Bowman Bottom Dweller's Avatar
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    Quote Originally Posted by Bottom Dweller View Post
    20%
    Sorry too quick to post. Should be 40% or 2/5.
    Archery's a lot like Life .... a few see it as an opportunity to score cheap points; while the rest are focused on the ends that count.
    Genesis 21:20 And God was with the boy as he grew up in the wilderness. He became a skillful archer.

  19. #18
    digitus impudicus
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    Quote Originally Posted by DaddyDugong View Post
    66.66% recurring
    WE HAVE A WINNER!

    Please show your working..
    Status is not defined by the amount of gear in your signature.
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  20. #19
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    Quote Originally Posted by Andy! View Post
    WE HAVE A WINNER!

    Please show your working..
    We start with 3 tubes - note: T = Tunsgten, S = Stainless

    (TT) (SS) (TS)

    as we have already chosen a tube which has a Tungsten point, we no longer need to include the tube with SS points

    (TT) (TS)

    Now we have removed one tungsten point from the equation. It doesn't matter which one we have removed.

    (_T) (TS) or (TT) (_S)

    we will always have a 2 out 3 chance that the second arrow left in that tube is a Tungsten.

  21. Thanks Andy! thanked for this post
  22. #20
    Learning the Ropes
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    Quote Originally Posted by DaddyDugong View Post
    We start with 3 tubes - note: T = Tunsgten, S = Stainless

    (TT) (SS) (TS)

    as we have already chosen a tube which has a Tungsten point, we no longer need to include the tube with SS points

    (TT) (TS)

    Now we have removed one tungsten point from the equation. It doesn't matter which one we have removed.

    (_T) (TS) or (TT) (_S)

    we will always have a 2 out 3 chance that the second arrow left in that tube is a Tungsten.
    Kudos for getting in with the right answer first, but I find your explanation a bit unconvincing.

    The way I see it: if A has TT and B has TS (the 3rd tube is irrelevant) and the first sample is T then it is twice as likely that we have tube A compared with tube B, because tube A had twice the proportion of arrows in it. That means 2/3 chance we have tube A and 1/3 chance we have tube B.

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