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Suppose I throw a fair die, and then you throw the fair die. What is the probability that your number is strictly greater than mine?

 Jun 26, 2020
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Suppose I throw a fair die, and then you throw the fair die. What is the probability that your number is strictly greater than mine? 

 

Make a grid as shown below.  These 36 groups represent every possible pair of throws. 

In each group, call the first number your throw and the second number my throw. 

Count the ones where the second number is strictly greater than the tirst. 

 

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 

 

You see there are 15 such groups that satisfy the requirement.  So the probability is 15/36, or 5/12

.

 Jun 26, 2020

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