Question

I have two dice, one red and one blue. when the two dice are rolled, the probability that the number showing on the red die is larger than the number showing on the blue die si

Answer 1

Total possible outcomes are= 6×6=36

For example, if you roll a 1 on the blue dice, you cannot roll another 1 (since 1 is not bigger than 1). 

Rolling a 2, you'd have 4 possible choices left (you cannot roll a 1 or 2 since they are less than 2). 

(1/6)<-- picking a 1/2/3/4/5/6 out of everything;

(1/6)(5/6)=5/36 <-- (5/6) possibilities of picking a number bigger than 1
(1/6)(4/6)=4/36 <-- (4/6) possibilities of picking a number bigger than 2
(1/6)(3/6)=3/36
(1/6)(2/6)=2/36 
(1/6)(1/6)=1/36 
(1/6)(0)=0 <-- Impossible to get a number bigger than 6 in a normal dice 

Add all of them together; 

(5+4+3+2+1+0)/36=15/36

Therefore, there are 15/36 possibilities of the red die showing a number larger than that of the blue die. 

Hope I helped :)