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Thread: Math Probabilities Qn

  1. #1
    vince123123
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    Default Math Probabilities Qn

    need to enlist the aid of those who still can remmeber probabilities....i returned all to the teacher years ago :P

    anyway the qn is, if i throw three dice, whats the probability that at least ONE of them will show a certain number that i picked. e.g. i pick number 6. whats the probability that at least ONE of them will show a 6?

    b) how about 2 of them?

    hope to get some answers! cheers!

  2. #2
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    My answers:
    a) 1/6+1/6+1/6 = 1/2

    taking b to mean three dice thrown, two giving the same number selected.
    b) 1/6*1/6+1/6*1/6+1/6*1/6 = 1/12

    might be a bit wrong though due to some overlap.
    Last edited by mpenza; 20th September 2004 at 10:47 AM.

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    try again:

    b) 1/6*1/6*5/6+1/6*1/6*5/6+1/6*1/6*5/6+1/6*1/6*1/6=0.074074

    a) 1/6*5/6*5/6+1/6*5/6*5/6+1/6*5/6*5/6+ b = 0.4213

  4. #4
    vince123123
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    hehe i initially thot the answer was 1/2 also in (a). but i realised that it can't be, cos if using that working, throwing 6 dice gives a probability of 1 to get the number

    Quote Originally Posted by mpenza
    My answers:
    a) 1/6+1/6+1/6 = 1/2

    taking b to mean three dice thrown, two giving the same number selected.
    b) 1/6*1/6+1/6*1/6+1/6*1/6 = 1/12

    might be a bit wrong though due to some overlap.

  5. #5
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    Use counting methods instead of probability. Sure correct one.

    3 dice gives 6x6x6 = 216 possible combinations (use a spreadsheet if you need). Out of these 216, 91 combinations contain the number 6. Therefore, the answer is 91/216.

    1/2 is the wrong answer bcoz it does not take overlapping solutions into account.
    Last edited by ST1100; 20th September 2004 at 11:28 AM.

  6. #6
    vince123123
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    wah how did you figure that out so fast? :P how u get the ez way to come up with all the combos?

    Quote Originally Posted by ST1100
    Use counting methods instead of probability. Sure correct one.

    3 dice gives 6x6x6 = 216 possible combinations (use a spreadsheet if you need). Out of these 216, 91 combinations contain the number 6. Therefore, the answer is 96/216.

    1/2 is the wrong answer bcoz it does not take overlapping solutions into account.

  7. #7
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    Quote Originally Posted by ST1100
    Use counting methods instead of probability. Sure correct one.

    3 dice gives 6x6x6 = 216 possible combinations (use a spreadsheet if you need). Out of these 216, 91 combinations contain the number 6. Therefore, the answer is 96/216.

    1/2 is the wrong answer bcoz it does not take overlapping solutions into account.
    same answer as mine yup, working out the combinations is a sure way to get the answer but it might be quite tedious for cases which have a lot more combinations.

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    Quote Originally Posted by vince123123
    wah how did you figure that out so fast? :P how u get the ez way to come up with all the combos?
    Erm, i did it mentally, but for 2 or more numbers, i would use a spreadsheet:

    1 1 1
    1 1 2
    1 1 3
    1 1 4
    ...
    ...
    6 6 3
    6 6 4
    6 6 5
    6 6 6


    If you know some excel programming, you can get excel to do the counting for you too.

    (Actually, i'm still trying to think of a correct way to calculate this using probablity instead of counting.)

  9. #9
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    Ok, the way to do it with probabilities:

    There is a 5/6 chance that there is no 6 on the first dice, and 5/6 chance on the second and third. Therefore, the answer is 1-(5/6^3).

  10. #10
    vince123123
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    wah not bad, so far there are 3 diff workings and all get hte same answer

    thanks guys!

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    this is a faster than what I've calculated

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    wahh.. probability.. did that last time ... for statistics classes...

    Headache ...

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    ClubSNAP Idol Adam Goi's Avatar
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    Well done! As an ex-Statistics major, for a while I did not know how and where to start!

  14. #14

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    Quote Originally Posted by AdamGoi
    Well done! As an ex-Statistics major, for a while I did not know how and where to start!
    tsk tsk. hahah, return all to teacher liao ar?

  15. #15

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    damn...where's my maths....

  16. #16
    ClubSNAP Idol Adam Goi's Avatar
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    Quote Originally Posted by simplicity_
    tsk tsk. hahah, return all to teacher liao ar?
    No ... I am a teacher who has lost it!

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    Quote Originally Posted by AdamGoi
    No ... I am a teacher who has lost it!
    even worst...

    heehee..

    Btw... you graduated with a degree in statistics?

  18. #18

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    Quote Originally Posted by AdamGoi
    No ... I am a teacher who has lost it!
    hahaha..

    haiyoh.. jia lat leh, liddat.

  19. #19

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    visualise a tree diagram,...each die giving off to 6 branches, it'll be easy.

    ST1100's answer using P(an event) = 1 - P(all other events) = 1-(5/6^3) is the quickest.

  20. #20
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    BTW, the answer for picking two numbers is 1-(4/6 ^3).

    Generic formula is 1-((6-r)/6 ^ d), where r is the number of picks and d the number of dice.

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