Explain this riddle answer

forever saving on 08/04/2014 - 09:37
Last edited 08/04/2014 - 09:48

This was from a free amazon riddle book posted on OzB - here

If anyone else wants to use this post for other riddles they didn't understand go ahead.

#18 Stones, Jars, Life and Death

So the riddle basically has 2 Jars. 1 filled with 100 black stones and the other filled with 100 white stones. You can change the composition of the 2 jars to whatever ratio you like however, at the end there must be 100 stones in each Jar. The Jars are shaken up.

You are then given 1 Jar at random and pick a stone out. If it is black you die, if it is white you live. How do you distribute the stones in order to give you the highest possibility of living?

SPOILER - ANSWER IS BELOW

So the book says to put 1 white stone in 1 jar and 99 white stones in the other for a success rate of 74.74%.
But it doesn't explain it at all like the other riddle solutions.
If you had put 100 white stones in 1 Jar - the probability is 50% flat.
I'm definitely missing something here, it's probably blindingly obvious.

General Discussion

Comments

  • Mikinoz on 08/04/2014 - 09:40
    +1

    Put the black stones on the bottom of the jars, white on top.

    • forever saving on 08/04/2014 - 09:45

      The Jars are shaken up such that you can't do that. I'm certain this has something to do with maths.

  • bittervalue on 08/04/2014 - 09:51
    -1

    Half the time (P=50%) the first jar will be picked, from which ONLY (100%) a black marble can be drawn. (P=50*100/100 = 50%)

    Half the time (P=50%) the second jar will be picked, from which there is a 49/(49+50) (=49.49%) chance of drawing a white marble. (P= 50*49.49/100 = 24.74%)

    Therefore the total probability of drawing a white marble is 50 + 24.74 = 74.74%

    • forever saving on 08/04/2014 - 10:01

      Thanks for your input. The first jar has 1 white stone so you can't say it's 100% a black marble will be drawn.

      Also, this doesn't make sense because by your logic the probability of drawing a black stone is also 74.74%.

    • retiredfeline on 08/04/2014 - 11:28

      So looks like you almost had the right solution (black -> white in your first paragraph) but it was for the right version of the riddle, not the one stated by the e-book author.

  • retiredfeline on 08/04/2014 - 10:00
    +2

    There's something missing in the riddle description. As stated it's 50% flat no matter what you do.

    • forever saving on 08/04/2014 - 10:05

      I would've written the whole thing but it's too long. It's mostly setting the scenario. King sentencing you to die. The pots are made of clay.. etc.

      The answer is actually stated in the book as 74.74% so it's no random fact stated somewhere in the riddle skewing this.

      • retiredfeline on 08/04/2014 - 10:26

        Maybe there was a second draw or something like that?

        But it's not unusual for "authors" to crib material from older sources for a compilation and miss some essential detail that makes the material just plain wrong.

  • brownbag on 08/04/2014 - 10:24

    According to the books' solution, your probability of getting a white stone is (0.5 x 0.01)+(0.5 x 0.99) You don't technically need the parenthesis but they make it easier to read.
    The odds of living if you are unlucky enough to get the jar with one white stone is 0.01.
    The odds of living if you are lucky enough to get the jar with 99 white stones is 0.99.

    There is a 50/50 chance you'll get one jar or the other, sot the total odds are (0.5 x 0.01)+(0.5 x 0.99), which equals 0.5.

    There's something missing.

  • geek001 on 08/04/2014 - 10:34

    I remember this being one of the recruitment questions for Google or Apple, can't remember which one. The answer is correct. I think you must be interpreted some of the rules in the question incorrectly. Either that or the author framed the question incorrectly?

    • forever saving on 08/04/2014 - 10:37

      This is what is annoying me, the book gives no rationale only the distribution and percentage.

      • geek001 on 08/04/2014 - 10:49
        +6

        I think your riddle should have been this:

        http://www.brainbashers.com/showanswer.asp?ref=ZNSX

      • donga100 on 08/04/2014 - 10:49
        +1

        It would be correct if you didn't need to have 100 stones in each jar. For example, first jar has just 1 white stone and second jar has 99 white and 100 black stones.

        • brownbag on 08/04/2014 - 10:52

          That makes perfect sense. And the result would be (0.5 x 100) + (0.5 x 99/199) = 74.74%

        • brownbag on 08/04/2014 - 10:57

          Yes Kingville, I did calculate 74.87 but ignored it. You're right. The riddle is totally wrong - I don't think I'll bother with the ebook!

  • kingsville on 08/04/2014 - 10:54
    +2

    I think the question is slightly wrong and shouldn't include "at the end there must be 100 stones in each Jar"

    If you can distribute stones as you please:
    *put 1 white in one jar
    *put 99 white and 100 black in other jar

    Chance of survival is (0.5 x 100%) + (0.5 x 49.75%) = 74.87%

    If you say there is 50 of each stone types then chance of survival is (0.5 x 100%) + (0.5 x 49.49%) = 74.7475%

    Perhaps this question phrases it better:
    http://www.braingle.com/wii/brainteasers/teaser.php?id=15446…

    edit: too slow :(

  • forever saving on 08/04/2014 - 11:04

    Yes it seems the book has morphed many of the existing riddles into it's own version. IT is a another version of the Life or Death riddle.
    Thanks all, no longer confused about it.

  • goosegog on 08/04/2014 - 13:47

    Don't do it in the first place! Are you all trying to find out when you will die ?

  • kwaker on 10/04/2014 - 09:26
    +2

    Cant you look before you pick the stone?

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