# Thread: Need some help with probability and dice

1. ## 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!

2. ## 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 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,

And similar for other cases.

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Tucker (07-10-2014)

4. ## 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

5. ## 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.

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