Step 1: Understand the given question and make a note of the all possible outcomes.

NOTE: A die is thrown twice.

So, Total number of event n(T) = 6 * 6 = 36

Let us consider an event A of getting number 5 on at least one dice

Events of getting 5 are n(F)= {(5,1),( 5,2),( 5,3),( 5,4),( 5,5),( 5,6),(1,5),(2,5),(3,5), (4,5),( 6,5)} = 11

Step 2: Verify that the given two events are complementary events are not.

NOTE: The given two events are compliment to each other

So, Probability of getting getting 5 = \frac{n(F)}{n(T)}

= \frac{11}{36}

Let us consider an event B of not getting number 5 either time

The probability of not getting 5 either time P(B) = 1 - P(A)

P(B) = 1 - \frac{11}{36}

= \frac{11 - 36}{36}

P(B) = \frac{25}{36}