Probability problem...the sequel

This is a discussion on Probability problem...the sequel within the Off Topic & Humor Discussion forums, part of the The Back Porch category; Since we had so much fun(?) with the Wild West probability problem, here is another one. You are a condemned man, sentenced to die by ...

Page 1 of 2 12 LastLast
Results 1 to 15 of 24

Thread: Probability problem...the sequel

  1. #1
    VIP Member
    Array OPFOR's Avatar
    Join Date
    Dec 2006
    Location
    Nomad
    Posts
    4,609

    Probability problem...the sequel

    Since we had so much fun(?) with the Wild West probability problem, here is another one.

    You are a condemned man, sentenced to die by firing squad. The executioner, however, used to me a mathematician, and has a sense of humor. He sets before you 100 bullets, 50 of them live and 50 "dummy." There is no way to tell by feel which is which. He also sets before you two bowls.

    "Here," he says. "Put all 100 bullets into these two bowls, in any configuration you want. I will then blindfold you, stir the contents of the bowls, an put them back in front of you. I will not move any bullets from the bowls. You must then select ONE bullet from ONE of the bowls - that is the bullet that will be fired at you. If it is a dummy, you live; if it is a live round, you die. Ready?"

    How do you place the bullets into the bowls in order to give yourself the best chance of drawing a "dummy," and saving your life?
    A man fires a rifle for many years, and he goes to war. And afterward he turns the rifle in at the armory, and he believes he's finished with the rifle. But no matter what else he might do with his hands - love a woman, build a house, change his son's diaper - his hands remember the rifle.

  2. Remove Ads

  3. #2
    VIP Member
    Array Hopyard's Avatar
    Join Date
    Jun 2006
    Location
    Disappeared
    Posts
    11,158
    in any configuration you want.

    you must then select ONE bullet from ONE of the bowls

    Any configuration you want but you must select one bullet from one of the bowls suggests you could put 99 bullets in one bowl and one bullet in the other.

    If you did that you'd have a 50:50 chance of having picked a dud. That's the same as if you just reached in and randomly selected one from the pile of 100--with 50 live and 50 duds.

    But, I'm thinking there must be some other answer because the executioner's job is to assure the deed gets accomplished, so the game has to be rigged so no matter what the guy does, he gets it.

    I think the executioner lied.

  4. #3
    Senior Member Array Rob P.'s Avatar
    Join Date
    Sep 2007
    Location
    In the sticks
    Posts
    631
    Put all the live rounds in one bowl and the inert round sin the other. No matter which bowl you choose from your odds are 50/50 that its the inert ammo bowl.

    Mixing the rounds in both bowls will not give you any better odds.

  5. #4
    Senior Moderator
    Array pgrass101's Avatar
    Join Date
    Sep 2006
    Location
    Alabama
    Posts
    13,087
    put 100 bullets in one bowl and 0 in the other, then choose the bowl with no bullets in it.

    But it can't be that easy
    Sometimes I wonder who the old man in the mirror is....

    Lord, Grant me a good sword and no need to use it.

  6. #5
    Member Array SAMI's Avatar
    Join Date
    Jan 2010
    Location
    Utah
    Posts
    216
    I'd imagine that by dropping the bullets into the bowl the dummies vs live would have a slightly different sound when they hit the bowl.

    Perhaps drop each round in the bowl, and put the ones that sound more solid/heavier in one bowl, and the lighter sounding ones in one bowl?

    You might be able to increase your odds that way.. THen you still have to choose which bowl to select from. I'd remove half of the dummies from the suspected dummy bowl after i'd sorted them, that way I know which bowl I want to select from since it has substantially less rounds in it...

    That's the best I can do without too much brain power.
    Forget 'Twitter', i'm on the CB...
    Cruiser Outfitters
    Utah Firearm
    Expedition Utah

  7. #6
    VIP Member
    Array Hopyard's Avatar
    Join Date
    Jun 2006
    Location
    Disappeared
    Posts
    11,158

    re: prgrass101

    Quote Originally Posted by pgrass101 View Post
    put 100 bullets in one bowl and 0 in the other, then choose the bowl with no bullets in it.

    But it can't be that easy
    I started off thinking that one too, but then re-read what the executioner said, "You must then select ONE bullet from ONE of the bowls." That seems to mean there must be at least one bullet in one of the bowls. At that point, the odds still seem to be 50:50.

    Until the OP provides the answer I stand by, "the executioner lied."

  8. #7
    Senior Member Array ZX9RCAM's Avatar
    Join Date
    Sep 2009
    Location
    The Woodlands, Texas
    Posts
    918
    subscribed......
    If there are no dogs in Heaven, then when I die I want to go where they went.

    -Will Rogers

    Im a big fan of the .22LR for bear defense.
    Just shoot the guy next to you in the knee and run like heck.

  9. #8
    VIP Member
    Array OPFOR's Avatar
    Join Date
    Dec 2006
    Location
    Nomad
    Posts
    4,609
    This is a "pure" math problem - disregard any attempts to "game" the answer by some other method. Assume there is no way to tell the difference between the live and dummy rounds until the trigger is pulled.

    And, obviously, since I posted the problem, there is an answer that will satisfy the problem. One point of clarification, though:

    You will not know what bowl you are drawing from until you reach into it; that is, you must first choose a bowl (blindfolded and with no way of knowing which bowl is which), and then choose a round from that bowl.
    A man fires a rifle for many years, and he goes to war. And afterward he turns the rifle in at the armory, and he believes he's finished with the rifle. But no matter what else he might do with his hands - love a woman, build a house, change his son's diaper - his hands remember the rifle.

  10. #9
    Senior Member Array TheGreatGonzo's Avatar
    Join Date
    Dec 2004
    Posts
    1,086
    Math problems are cruel and unusual punishment. Just shoot me, please...
    "Skin that smokewagon!".

  11. #10
    VIP Member Array HKinNY's Avatar
    Join Date
    Dec 2007
    Location
    Nassau, NY(Long Island)
    Posts
    2,855
    Way off topic for a minute.

    I have an uncle who is an electrician for 40 years. He was hired to hook up an expensive chandelier that came from over seas. It had 100 same colored wires. His helper Freddie Noonie from Ireland stripped all 100 wires. The helper took 50 in one hand and 50 in the other and twisted the wire nuts on and flipped the switch and all the lights worked and did not pop the breaker. My uncle stood there mouth agape. If one if the connections were wrong the breaker would have popped. Freddie would not tell how he did it. My uncle had to wait 18 months until he did something that Freddie could not do. Then they traded secrets.

    Back onto the topic. So when you tell me how to choose the correct bullet, I will tell you how to wire a 100 wire chandelier.

  12. #11
    Distinguished Member Array kazzaerexys's Avatar
    Join Date
    Nov 2007
    Location
    Maryland
    Posts
    1,838
    Quote Originally Posted by OPFOR View Post
    How do you place the bullets into the bowls in order to give yourself the best chance of drawing a "dummy," and saving your life?
    Okay...

    If I am allowed to put zero bullets in a bowl (meaning if I draw that bowl I go scot free), then I put all 100 in one bowl and none in the other. Then my probability of pulling a live round is only 25% (50% chance of choosing the full bowl, and 50% of those being live rounds).

    Thus, I have a 75% chance of living.

    Now, if that's not an allowable solution, then I am invoking the Law of Total Probability and getting about waist deep in factorial expansions...

    Do I need to keep working, or is this the solution?
    “What is a moderate interpretation of [the Constitution]? Halfway between what it says and [...] what you want it to say?” —Justice Antonin Scalia

    SIG: P220R SS Elite SAO, P220R SAO, P220R Carry, P226R Navy, P226, P239/.40S&W, P2022/.40S&W; GSR 5", P6.

  13. #12
    VIP Member Array Hiram25's Avatar
    Join Date
    Feb 2010
    Location
    Wyoming, DE
    Posts
    10,778
    It doesn't matter what you do with the bullets. You are to be shot by a "Firing Squad" squad means at least more than one person. Since the "Firing Squad" is not supposed to know who fired the fatal shot, and only one bullet is to be used the "Firing Squad" will not be able to shoot you.

    What was the question?

  14. #13
    VIP Member
    Array OPFOR's Avatar
    Join Date
    Dec 2006
    Location
    Nomad
    Posts
    4,609
    Well, in my answer, you have to put at least one round into each bowl. That said, your answer is correct: put ONE dummy round into one bowl, then the rest into the other. That way, you have a 50% chance of choosing the bowl with the dummy round in it, so you're home free. If you miss that, you still have a 49/99 chance (or very nearly 50%) chance of drawing a dummy round from the other bowl. So, your chances are nearly 75% to survive...

    I knew you'd get the gist, Kazz!
    A man fires a rifle for many years, and he goes to war. And afterward he turns the rifle in at the armory, and he believes he's finished with the rifle. But no matter what else he might do with his hands - love a woman, build a house, change his son's diaper - his hands remember the rifle.

  15. #14
    VIP Member
    Array OPFOR's Avatar
    Join Date
    Dec 2006
    Location
    Nomad
    Posts
    4,609
    Quote Originally Posted by Hiram25 View Post
    It doesn't matter what you do with the bullets. You are to be shot by a "Firing Squad" squad means at least more than one person. Since the "Firing Squad" is not supposed to know who fired the fatal shot, and only one bullet is to be used the "Firing Squad" will not be able to shoot you.

    What was the question?
    Nice try, but I explained that this was a math/probability problem, not a "game the wording problem..."
    A man fires a rifle for many years, and he goes to war. And afterward he turns the rifle in at the armory, and he believes he's finished with the rifle. But no matter what else he might do with his hands - love a woman, build a house, change his son's diaper - his hands remember the rifle.

  16. #15
    VIP Member Array Hiram25's Avatar
    Join Date
    Feb 2010
    Location
    Wyoming, DE
    Posts
    10,778
    Quote Originally Posted by OPFOR View Post
    Nice try, but I explained that this was a math/probability problem, not a "game the wording problem..."
    It was worth a shot!

Page 1 of 2 12 LastLast

Links

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  

Similar Threads

  1. Even easier probability problem(s)...
    By OPFOR in forum Off Topic & Humor Discussion
    Replies: 23
    Last Post: April 25th, 2010, 07:42 PM
  2. Probability 101: Monty Hall
    By OPFOR in forum Off Topic & Humor Discussion
    Replies: 88
    Last Post: April 25th, 2010, 03:41 PM
  3. CCW problem for
    By jordanasm in forum Defensive Carry Holsters & Carry Options
    Replies: 25
    Last Post: July 20th, 2009, 02:49 PM
  4. Equipment Problem or Training Problem -- Boston PD Melts Down Pepper-pellet Guns
    By SIGguy229 in forum Law Enforcement, Military & Homeland Security Discussion
    Replies: 11
    Last Post: February 25th, 2007, 02:59 PM

Search tags for this page

probability of a dud bullet

Click on a term to search for related topics.