Two dice each numbered 1, 2, 3, 4, 5, 6 and 1,1,2,2,3,3 . . .

Question : Two dice each numbered 1, 2, 3, 4, 5, 6 and 1,1,2,2,3,3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately. 

Doubt by Lavanya

Solution : 
Total possible outcomes 
{

(1,1), (1,1), (1,2), (1, 2), (1,3), (1,3)

(2,1), (2,1), (2,2), (2, 2), (2,3), (2,3)

(3,1), (3,1), (3,2), (3, 2), (3,3), (3,3)

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

(6,1), (6,1), (6,2), (6, 2), (6,3), (6,3)
} = 36

P(E) = No. of favourable outcomes / Total number of possible outcomes

No. of outcomes when sum on both the dice is 2 {(1,1), (1,1)} = 2

P(Sum is 2) = 2/36 = 1/18

No. of outcomes when sum on both the dice is 3 {(1,2), (1, 2), (2,1), (2,1)} = 4

P(Sum is 3) = 4/36 = 1/9

No. of outcomes when sum on both the dice is 4 {(1,3), (1,3), (2,2), (2, 2), (3,1), (3,1)} = 6

P(Sum is 4) = 6/36 = 1/6

No. of outcomes when sum on both the dice is 5 {(2,3), (2,3), (3,2), (3, 2), (4,1), (4,1)} = 6

P(Sum is 5) = 6/36 = 1/6

No. of outcomes when sum on both the dice is 6 {(3,3), (3,3), (4,2), (4, 2), (5,1), (5,1)} = 6

P(Sum is 6) = 6/36 = 1/6

No. of outcomes when sum on both the dice is 7 {(4,3), (4,3), (5,2), (5, 2), (6,1), (6,1)} = 6

P(Sum is 7) = 6/36 = 1/6

No. of outcomes when sum on both the dice is 8 {(5,3), (5,3), (6,2), (6, 2)} = 4

P(Sum is 8) = 4/36 = 1/9

No. of outcomes when sum on both the dice is 9 {(6,3), (6,3)} = 2

P(Sum is 9) = 2/36 = 1/18