If I roll two sets of 6 dice what are the odds of both sets of dice showing identical numbers?
I believe the 1 in 36 is the odds for two dice being the same number. If I times thse odds by 6 the odds would become 1 in 216 is this the correct answer?
Just for clarification. I rolled two sets of 6 standard 6 sided dice (e.g.total 12 dice)
The first set of 6 matched the second set of 6
I want the odds of rolling two matching sets.
this question is poorly worded.
If you are asking something special, like "if I rolled 6 4's last roll, what are the odds of doing it again?"
That's 1 in 6^6 = 1 in 46,656
And asking "what if I rolled 2 6 of a kinds of the same number in 2 consecutive rolls" is:
1 in 6^11 = 1 in 362.8 million
1 in 6^5 for the first number (can be any number) times 1 in 6^6 for the 2nd number (since it must be the same number as first rolled number)
But what if your question is more general?
Let's say you roll 3 1 4 2 5 5 on roll one.
What if you ask "what are the odds of rolling 3 1 4 2 5 5 on the next roll?"
The dice order doesnt matter here. So there are 6!/2! = 6*5*4*3*2*1/(2*1) = 360 ways to order this roll of the dice (the 2! comes from the 5's repeating) see http://www.andrews.edu/~calkins/math/webtexts/prod02.htm for more info
The probability of the roll given the first roll is 1 in 6^6 if order of the dice mattered. So the probability of rolling 3 1 4 2 5 5 again after rolling it once is 360/6^6 = 360/46,656 = 1 in 129.6
Here is an example with 2 pairs:
5 5 3 3 2 6 = 6!/2!/2! = 180 ways to order the numbers
Probability of rolling this again on the next roll:
180/6^6 = 1 in 259.2
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