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Alli rolls a standard 6-sided die twice. What is the probability of rolling integers that differ by 2 on her first two rolls? Express your answer as a common fraction.

 Aug 16, 2022
 #1
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(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5)>>Total = 36

 

 

The probability is: 8 / 36 ==4 / 9

 Aug 16, 2022
 #2
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8/36 simplifies to 2/9

bobjohnson  Aug 16, 2022
edited by bobjohnson  Aug 16, 2022
 #3
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Alli rolls a standard 6-sided die twice. What is the probability of rolling integers that differ by 2 on her first two rolls? Express your answer as a common fraction.  

 

Here are all the pairs of rolls that Alli could roll, 36 of them. 

The highlighted pairs are the ones that satisfy the condition. 

 

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 

 

Out of a possible 36 pairs, 8 satisfy the required condition.  8/36  reduces to  2/9  

.

 Aug 18, 2022

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