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August 27th, 2017, 05:39 PM  #1 
Newbie Joined: Aug 2017 From: Hong Kong Posts: 3 Thanks: 0 Math Focus: Calculus  Dice question, roll a double triple twice in a row
New question... 6 dice. What are the odds of rolling a douple triple twice in a row? Example: First roll is 222333. Next roll is also a double triple; say 111666. Thanks, Matt Last edited by Toucanf16; August 27th, 2017 at 05:42 PM. 
August 27th, 2017, 06:20 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,415 Thanks: 830  
August 27th, 2017, 07:32 PM  #3 
Newbie Joined: Aug 2017 From: Hong Kong Posts: 3 Thanks: 0 Math Focus: Calculus 
Yes, The roll can be any combination as long as it's three of one number and three of another number.

August 27th, 2017, 07:34 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 1,939 Thanks: 1006  Quote:
$aaabbbcccddd$ where it's possible that triplets repeat. there are $6^{12}$ total roll combinations of those $6^4$ will have the above pattern. so $p = \dfrac{6^4}{6^{12}} = 6^{8} \approx 5.59\cdot 10^{7}$  
August 27th, 2017, 07:50 PM  #5 
Newbie Joined: Aug 2017 From: Hong Kong Posts: 3 Thanks: 0 Math Focus: Calculus 
Romsek, thanks! Matt 
August 29th, 2017, 11:04 AM  #6 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361 
I get 101^2 / 6^10 = 0.000168705... = 1.68705... * 10^4. Hope we did the same interpretation of the question! The change of rolling a double triple is 101/6^5; say the double triple is aaabbb Then, if a = b, we have aaaaaa which happens in $\displaystyle \frac{6}{6^6} = \frac{1}{6^5}$ of the time OR if a isn't b, we have aaabbb which can be arranged in $\displaystyle {6 \choose 3} = 20$ ways. This happens in $\displaystyle \frac{6 \cdot 5 \cdot {6 \choose 3}}{6^6} = \frac{100}{6^5}$ This adds to a total of $\displaystyle \frac{101}{6^5}$ Rolling a double triple is independent from earlier rolls so we can use the productrule for probabilities which says the answer is $\displaystyle \left( \frac{101}{6^5} \right)^2 = 1.68705... \cdot 10^{4}$ 

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dice, double, question, roll, row, trip, triple 
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