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Blatherings

Math Problem!
Previous | Next by elfie 11 February, 2011 - 9:42 AM

You roll 3D6 (three six-sided dice), two are black and one is green.

1) What is the chance that you will roll doubles (any two dice match)?
2) What is the chance that the green die matches either of the black ones?
3) What is the chance that the two black dice match?

Rolling three-of-a-kind still qualifies as rolling doubles. Present all answers as a percentage. Show your work (as much as HTML will allow).




2/11/2011 >> mike

It's been a long time since I took logic, probability, and statistics, but I think the answers are 1) 66% 2) 33% 3) 17%


2/11/2011 >> elfie

3 seems right to me, but I think 1 is kinda high. That's why I asked you to show your work :)


2/11/2011 >> ben

i was too lazy to type out all of my work, but i got #1 for you right here


2/11/2011 >> muhgcee

1) You need to add up the chances that #1 matches #2, or #1 matches #3, or #2 matches #3. The chance of any one of these happening is 1/6. Adding that up, it is 3/6 or 50%. The problem is that within all of these chances there is also the possibility that all three dice will match. Since we only want to count this occurrence once, and we have counted it three times above. So let's subtract 2/18 from the above answer giving 7/18 or 38.9%. I think I got this one wrong.
2) There are two situations here. Either the black dice match or they don't. There is a 1/6 chance that the black dice match. There is further a 1/6 chance that the green die also matches. So 1/6 x 1/6 = 1/36. The second situation is if the black dice do not match. There is a 5/6 chance of this happening. Within this situation, there is a 1/6 chance that the green die matches black die #1 and a 1/6 chance that the green die matches black die #2. You have to add these two, and multiply by 5/6. So you have (1/3) x (5/6) = 5/18. Add this 5/18 to the 1/36 from above and you get 11/36 or 30.6%
3) This one is easy. The first black die can be anything. There is a 1/6 percent chance that the second black die matches, or 16.7%


3/8/2011 >> muhgcee

I can't believe I did all that work and I don't even get a grade almost a month later. Harumph!


3/8/2011 >> elfie

haha well the problem is: who knows if you're right? I got several different answers all AROUND what your results were. So I just took those and forged ahead. I feel like the final tally was around 42%, 33%, 17%. Everyone was pretty solid on 33 and 17, but was a little fuzzy around the 42.


3/8/2011 >> muhgcee

Haha I figured you must have been reading it out of a Statistics textbook or something.


3/8/2011 >> ben

42 is ALWAYS the answer


3/8/2011 >> muhgcee

Ben, how old are you?


3/8/2011 >> ben

42, of course


3/8/2011 >> muhgcee

That's what I thought.


3/9/2011 >> elfie

Nope. No statistics textbook. I'm GM'ing Dragon Age, in which all rolls are based on 3D6 where one of them is off-colored (called the Dragon Die). "Stunt Points" are their version of critical hits and they are generated when you roll doubles during an attack roll. I wanted to figure out how often that really happened because I wanted to use the same effect for some other mechanics that I had made up.

Figuring straight up doubles were happening nearly 50% of the time, I wanted to see how rare I could make an effect under similar rules. So I came up with "Dragon Doubles" (doubles where one of the matches is the Dragon Die" and "Non-Dragon Doubles" (doubles where the two same-color dice match). I didn't change the existing Stunt Points rules, but I did use these two concepts for effects of my own design.




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