A red 6sided die and a green 6sided die are thrown simultane

A red 6-sided die and a green 6-sided die are thrown simultaneously. The outcomes of this experiment are equally likely. What is the probability that at least one of the dice lands with a 6 on its upper face?

Solution

Sample space = {(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)} = 36          

at least one of the dice lands with a 6 on its upper face = {
(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) } = 11

probability that at least one of the dice lands with a 6 on its upper face = 11/36