Question

Two dice are 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.

Answer 1

Favourable outcomes $=36$

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

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

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

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

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

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

the probability of getting each sum from 2 to 9

Sum of $2=\frac{2}{36}=\frac{1}{18}$

Sum of $3=\frac{4}{36}=\frac{1}{9}$

Sum of $4=\frac{4}{36}=\frac{1}{9}$

Sum of $5=\frac{6}{36}=\frac{1}{6}$

Sum of $6=\frac{6}{36}=\frac{1}{6}$

Sum of $7=\frac{6}{36}=\frac{1}{6}$

Sum of $8=\frac{4}{36}=\frac{1}{9}$

Sum of $9=\frac{2}{36}=\frac{1}{18}$.