A die is thrown twice. What is the probability that(i)   5 will not come up either time? (ii) 5 will come up at least once?[Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]

Solution: outcomes :
(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)
(i) no of outcomes= 25
P= $\frac{25}{36}$
(ii) no of outcomes = $1-25$
P= $1-\frac{25}{36}=\frac{11}{36}$