SOLUTION: Two dice (say one red and one white) are rolled. What is the probability that the white die turns up a smaller number than the red die ?

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Question 862801: Two dice (say one red and one white) are rolled. What is the probability that the white die turns up a smaller number than the red die ?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Assume that (M,N) in the chart below represents the case
where the red die turns up M and the white die turns up N.

(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) 

So the denominator of the desired probability will be 36.


We want to know the probability that white (2nd) dies turns
up a smaller number than the red (1st) die.  These successful
rolls are the one below.  Count them.  There are 15.


(2,1)  

(3,1) (3,2) 

(4,1) (4,2) (4,3)  

(5,1) (5,2) (5,3) (5,4)  

(6,1) (6,2) (6,3) (6,4) (6,5)

So the numerator of the probability is 15

So the desired probability is 15 out of 36 
or 15%2F36 which reduces to 5%2F12.

Edwin