Question

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is:
(i) 0
(ii) 12
(iii) less than 12
(iv) less than or equal to 12

Answer 1

Total numbers = 36 i.e.
(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) Favourable outcomes=0
P(E)= $\frac{0}{36}=0$
(ii) Favourbale outcomes= 1 i.e. (6,6)
P(E) = $\frac{1}{36}$
(iii) Favourbale outcomes= 35 [Except (6,6)]
P(E) = $\frac{35}{36}$
(iv) Favourbale outcomes= 36
P(E) = $\frac{36}{36}=1$