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
Tucker (07-10-2014)
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
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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