Two dice are thrown simultaneously. What is the probability that:

GIVEN: Two dice are thrown

TO FIND: Probability of the following:

Let us first write the all possible events that can occur

(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),

Hence total number of events is 

(i) Favorable events i.e. 5 will not come up on either of them

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

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

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

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

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

Hence total number of favorable events i.e. 5 will not come up on either of them is 25

We know that PROBABILITY = 

Hence probability that 5 will not come up on either of them is equal to

(ii) Favorable events i.e. 5 will come on at least once

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

Hence total number of favorable events i.e.5 will not come on at least once is 11

We know that PROBABILITY = 

Hence probability of getting i.e. 5 will come on at least once is equal to

(iii) Favorable events i.e. 5 will come on both side

is (5, 5)

Hence total number of favorable events i.e. 5 will come on both side is 1

We know that PROBABILITY = 

Hence probability of getting 5 will come on both side is equal to