Five Rolls
What is the probability of rolling a pair with five dice?
A pair is when you roll two dice of the five with the same number. The dice also is labelled 1 – 6
One pair means one set of dice that are them same not two not three just one. For example 1-1-2-3-4 or 2-2-1-4-5
Frankly I don’t feel like doing the math right now. Here are a couple thoughts, though:
First – does “rolling a pair” include rolling something like 2, 4, 4, 4, 5??? Or does that NOT count because it’s 3 of a kind?
Does it include rolling something like 1-1-3-3-6, or does that not count because it’s 2-pair??? Similar for 2-2-2-2-3, or 6-6-6-6-6. Do these combinations count as having rolled a pair?
Making this clear makes a difference. If you exclude all of the above examples, the probability is quite a bit lower.
One more point – If you include the above examples, the probability will be very high. You are much more likely to roll a pair than not. There are only 6 different combinations that do NOT include a pair: 1-2-3-4-5; 1-2-3-4-6; 1-2-3-5-6; 1-2-4-5-6; 1-3-4-5-6; and 2-3-4-5-6.
Now there are multiple ways these combinations can hit because ANY of the dice could be the “1″, or the “2″, or the “3″, etc. in any of the above examples, but still you’re very limited.
Just guessing, (again, ’cause I’m too lazy to do the math right now), but I’m thinking you’ll roll a pair close to 87% of the time – give or take 5%.
Looking forward to seeing the answer. If nobody comes up with it, ask this again in the mathematics area. (Is there a math area?!?) Don’t forget to make it more clear what can constitute a “pair”.
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