Question 862801
<pre>

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 {{{15/36}}} which reduces to {{{5/12}}}.

Edwin</pre>