+ Reply to Thread
Results 1 to 4 of 4

Thread: Need some help with probability and dice

  1. #1
    Points: 12, Level: 1
    Level completed: 23%, Points required for next Level: 38

    Posts
    2
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Need some help with probability and dice




    Hi guys,

    I'm making a board game and ran into some probability problems with dice. I use custom dice (green, blue, red, and yellow). The same event occurs on each color dice, but at different probabilities. I want to know how to calculate the probability that an event will occur 2 times when rolling X number of different colored dice.

    The probability of the event occurs on each dice as follows:
    Green: .16
    Blue: .25
    Red: .08
    Yellow: .33

    If I roll 2 green, 1 blue, 1 red, and 1 yellow, what's the probability of the event occurring 2 times?

    Thanks so much for your help!
    Last edited by Tucker; 07-09-2014 at 05:25 PM. Reason: Clarification

  2. #2
    TS Contributor
    Points: 22,410, Level: 93
    Level completed: 6%, Points required for next Level: 940

    Posts
    3,020
    Thanks
    12
    Thanked 565 Times in 537 Posts

    Re: Need some help with probability and dice

    There should be no elegant method to do it. All you need to do is to list out all \binom {5} {2} = 10 mutually exclusive cases and sum them up.

    E.g. One of the case could be the event occur on G2 and Y, but not on G1, B and R.

    Then the probability of this case will be, by independence,

    (1-.16) \times .16 \times (1 - .25) \times (1 - .08) \times .33

    And similar for other cases.

  3. The Following User Says Thank You to BGM For This Useful Post:

    Tucker (07-10-2014)

  4. #3
    Points: 12, Level: 1
    Level completed: 23%, Points required for next Level: 38

    Posts
    2
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Need some help with probability and dice

    Great! Thanks for the help. For the purpose of simplifying, if I reduced the number of dice to 4 and changed them to 2G and 2B dice, would the possible mutually exclusive cases you're referring to be what I've listed below?

    Assume dice are GGBB and Y means an event occurred and N means it did not:

    YYNN
    YNYN
    YNNY
    NYYN
    NYNY
    NNYY

    When I compute that I get:
    0.1667 * 0.1667 * 0.75 * 0.75=1.56%
    0.1667 * 0.8333 * 0.25 * 0.75=2.60%
    0.1667 * 0.8333 * 0.75 * 0.25=2.60%
    0.8333 * 0.1667 * 0.25 * 0.75=2.60%
    0.8333 * 0.1667 * 0.75 * 0.25=2.60%
    0.8333 * 0.8333 * 0.25 * 0.25=4.34%

    Total of 2 events occurring over 4 dice: 16.32%

    That seemed a little low, especially when I computed (probably incorrectly) that the probability of at least one event occurring at ~ 60%


    Edit: Also, I guess maybe that is finding exactly the probability of exactly 2 events happening, instead of 2 or more? If I wanted to add in the 'or more' part, I would add more cases for those, correct? Such as:
    YYYN
    YNYY
    YYNY
    YYYY
    NYYY
    Last edited by Tucker; 07-09-2014 at 09:59 PM. Reason: FUBAR

  5. #4
    TS Contributor
    Points: 22,410, Level: 93
    Level completed: 6%, Points required for next Level: 940

    Posts
    3,020
    Thanks
    12
    Thanked 565 Times in 537 Posts

    Re: Need some help with probability and dice


    Yes you are correct that in the previous post I am stating the way to calculate exactly 2 events happening but not 2 or more. For 2 or more events happening, it will be simpler to calculate 1 or less event happening.

+ Reply to Thread

           




Posting Permissions

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






Advertise on Talk Stats