Question

Match the following
A black die and a white die are thrown at the same time.

Answer 1

When two dice are thrown, the possible $36$ outcomes are

(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)

We get the sum $9$ when pair of outcomes are $(3,6),(6,3)(4,5),(5,4)$.
So, the probability of getting a total of $9=\frac{4}{36}=\frac{1}{9}$
We get the sum $10$ when pair of outcomes are $(5,5),(6,4)(4,6)$.
So, the probability of getting a total of $10=\frac{3}{36}=\frac{1}{12}$
Sum greater than $9$, means sum of $10,11,12$
We get it when the pair of outcomes are $(5,5),(6,4)(4,6);(5,6),(6,5);(6,6)$.
So, the probability of getting a total more than $9=\frac{6}{36}=\frac{1}{6}$
We get the sum $8$ when pair of outcomes are $(4,4),(5,3),(3,5),(6,2)(2,6)$.
So, the probability of getting a total of $8=\frac{5}{36}$
Hence, $A-4,B-3,C-1,D-2$