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When Colby rolls two fair standard dice, what is the probability that he rolls the same number on both dice or that the sum of the two numbers rolled is divisible by 3? Express your answer as a common fraction.

 Nov 12, 2020
 #1
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When Colby rolls two fair standard dice, what is the probability that he rolls the same number on both dice or that the sum of the two numbers rolled is divisible by 3? Express your answer as a common fraction.   

 

These are the that Colby could roll. 

The highlighted pairs fit a requirement. 

 

1,1   1,2   1,3   1,4   1,5   1,6  

2,1   2,2   2,3   2,4   2,5   2,6  

3,1   3,2   3,3   3,4   3,5   3,6  

4,1   4,2   4,3   4,4   4,5   4,6  

5,1   5,2   5,3   5,4   5,5   5,6  

6,1   6,2   6,3   6,4   6,5   6,6  

 

Looks like there are 16 of them, so the probability is 16 out of 36 - which reduces to 4/9    

.

 Nov 12, 2020
 #2
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36 possible rolls

  6 rolls of doubles are possible   2 2   1 1    3 3    etc

     roll 3 or a 6        1 2     2 1    5 1   1 5    4 2     2 4     3 3       12  out of 36    (don't count 3 3 twice !)

 Nov 12, 2020
 #3
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Error:   look at the FIRST answer....not the second one !

Guest Nov 12, 2020

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