Posers and Puzzles

Posers and Puzzles

  1. Joined
    16 Dec '04
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    2433
    29 Dec '04 12:36
    this is an easy one,

    you have 2 jars & 100 marbles, 50 red and 50 blue.

    you have to place the marbles into the jars such that you maximise the likelihood that you pick out a red marble.

    i can get almost 3/4 or 75% likelihood.
  2. Standard memberTheMaster37
    Kupikupopo!
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    29 Dec '04 13:23
    1 red marble in jar 1 and the rest in jar 2 gives about 3/4 chance...74/99 to be precise

    put x red marbles in jar 1 along with y black ones.

    With chance 1/2 you pick a marble from jar 1, with chance x/x+y this is a red marble.

    With chance 1/2 you pick a marble from jar 2, with chance 50-x/100-x-y this is a red marble.

    1/2*(x/x+y + 50-x/100-x-y) = ugly

    I have not the time to write ugly out, to differentiate to x and y and to see of they happen to have a common zero.
  3. Joined
    08 Jun '04
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    3351
    29 Dec '04 14:15
    Originally posted by kcams
    this is an easy one,

    you have 2 jars & 100 marbles, 50 red and 50 blue.

    you have to place the marbles into the jars such that you maximise the likelihood that you pick out a red marble.

    i can get almost 3/4 or 75% likelihood.
    The statement of your puzzle is incomplete. What , wherefrom and how do you pick out has to be specified.
  4. SubscriberAThousandYoung
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    30 Dec '04 04:00
    Originally posted by kcams
    this is an easy one,

    you have 2 jars & 100 marbles, 50 red and 50 blue.

    you have to place the marbles into the jars such that you maximise the likelihood that you pick out a red marble.

    i can get almost 3/4 or 75% likelihood.
    Place the red marbles into both jars. Give the blue marbles to the kid down the street. 100%.

    Place 25 blue marbles into each jar. Carefully, without disturbing the jars, place 25 red marbles on top of the blue marbles. 100%.
  5. Joined
    16 Dec '04
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    2433
    30 Dec '04 11:26
    Originally posted by cheskmate
    The statement of your puzzle is incomplete. What , wherefrom and how do you pick out has to be specified.
    you pick the jar and marble at random.
  6. Standard memberflexmore
    Quack Quack Quack !
    Chesstralia
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    18 Aug '03
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    30 Dec '04 11:37
    Originally posted by kcams
    this is an easy one,

    you have 2 jars & 100 marbles, 50 red and 50 blue.

    you have to place the marbles into the jars such that you maximise the likelihood that you pick out a red marble.

    i can get almost 3/4 or 75% likelihood.
    😕
  7. H. T. & E. hte
    Joined
    21 May '04
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    3510
    31 Dec '04 13:03
    Originally posted by kcams
    you pick the jar and marble at random.
    put 1 red marble in one jar and put all the rest in the other. The probability of picking a red marble would be;
    (1+49/50)/2 = 74.99%....This is the maximum that can be achieved.
  8. Dhaka
    Joined
    08 Oct '04
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    02 Jan '05 15:18
    Originally posted by ranjan sinha
    put 1 red marble in one jar and put all the rest in the other. The probability of picking a red marble would be;
    (1+49/50)/2 = 74.99%....This is the maximum that can be achieved.

    ????????????
    how?....
  9. SubscriberAThousandYoung
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    02 Jan '05 15:28
    There's a 50% chance you'll pick the jar with the red marble. If you pick this jar, you'll definitely get a red marble. (1/2)

    If you don't pick that jar, then you'll have a 49/100 chance of getting a red marble.

    Therefore the chance of getting a red marble is 1/2 + 1/2 * 49/100 = 100/200 + 49/200 = 149/200.
  10. Dhaka
    Joined
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    02 Jan '05 15:36
    expression was to be(1+(49/100))/2
  11. Joined
    31 Oct '04
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    2047
    03 Jan '05 07:471 edit
    Originally posted by muktadir
    The second box contains 99 marbles, out of which 49 are red. Hence actually it will obviously be -
    (1+49/99)/2 = 74.99%...
  12. SubscriberAThousandYoung
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    03 Jan '05 09:05
    Originally posted by coolwarrior
    The second box contains 99 marbles, out of which 49 are red. Hence actually it will obviously be -
    (1+49/99)/2 = 74.99%...
    Oops
  13. H. T. & E. hte
    Joined
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    03 Jan '05 09:52
    Originally posted by muktadir
    It was a case of error due to hurried thinking and typing. Coolwarrior has already posted the correct expression. Thankx.
  14. Standard memberTheMaster37
    Kupikupopo!
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    12 Jan '05 19:23
    Originally posted by ranjan sinha
    It was a case of error due to hurried thinking and typing. Coolwarrior has already posted the correct expression. Thankx.
    *cough* In my days we were taught to simplify expressions like that.

    Correct me if i'm wrong but it's not 74.99%

    My calculation say it's 74/99 = 74.74 % approximately.
  15. H. T. & E. hte
    Joined
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    13 Jan '05 11:03
    Originally posted by TheMaster37
    *cough* In my days we were taught to simplify expressions like that.

    Correct me if i'm wrong but it's not 74.99%

    My calculation say it's 74/99 = 74.74 % approximately.
    put x = 1, and y = 0, in the expression (=ugly) given in your earlier post.
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