A pair of dice are rolled What is the probability that Exact

A pair of dice are rolled. What is the probability that Exactly one of them is a six?

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)}

Exactly one of them is a six ={(6,1),(6,2),(6,3),(6,4),(6,5),(1,6),(2,6),(3,6),(4,6),(5,6)}

P(Exactly one of them is a six) = 10/36 = 0.2778