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Wu rolls two fair, six-sided dice. You are not told what the rolls were, but you are told that the sum of the two rolls is a prime. What is the probability that the sum of the two rolls is $2$?

 Nov 25, 2021
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Wu rolls two fair, six-sided dice. You are not told what the rolls were, but you are told that the sum of the two rolls is a prime. What is the probability that the sum of the two rolls is $2$?  

 

There are 36 possible rolls, but only one of them totals 2. 

Therefore the probability is 1/36.  

 

Here is a table showing all 36 possible rolls. 

As you can see, there's only one way to get a 2.  

 

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  

 Nov 25, 2021

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