Please show all steps and reasoning Consider a throw of thre

Please show all steps and reasoning: Consider a throw of three normal dice (red, blue, and green). Call R, B and G the numbers you get on the three dice. Only considering those events for which R + B + G = 12, what is the probability distribution for R?

Solution

Only considering those events for which R + B + G = 12, those are:

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

then probability = 25/216