A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.

Solution:

GIVEN: A pair of dice is thrown

TO FIND: Probability that the total of numbers on the dice is greater than 9

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 

Favorable events i.e. getting the total of numbers on the dice greater than 9 are

(5,5), (5,6), (6,4), (4,6), (6,5) and (6,6),

Hence total number of favorable events i.e. getting the total of numbers on the dice greater than 9 is 6

We know that PROBABILITY = 

Hence probability of getting the total of numbers on the dice greater than 9 is