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 numbrees of them is noted. Find the probability of getting each sum from 2 to 9 separately.

Explanation

Total number of all possible outcomes, i.e., T(E) = 36
(i)Number of favourable outcome when
Sum of numbers on two dice is 2, i.e., (1,1),(1,1),
`therefore" "F(E) = 2 `
`rArr " "P_(1)(E)= (F(E))/(T(E)) = (2)/(36) = (1)/(18)`
(ii) Number of favourable outcomes when
Sum of number on two dice is 3, i.e., (1,2),(1,2),(2,1),(2,1)
`therefore " "F(E) = 4`
`rArr " "P_(2)(E) = (F(E))/(T(E)) = (4)/(36) =(1)/(9)`
(iii) Number of favourable outcomes when
Sum of number on two dice is 4, i.e., (1,3),(1,3),(2,2),(2,2),(3,1),(3,1).
`therefore" "F(E) = 6`
`rArr " "P_(3) (E) = (F(E))/(T(E)) = (6)/(36) = (1)/(6)`
(iv) Number of favourable outcomes when
Sum of numbers on the dice is 5,i.e, (2,3),(2,3),(3,2),(3,2),(4,1),(4,1)
`therefore " "F(E) = 6`
` rArr " "P_(4) (E) = (F(E))/(T(E)) = (6)/(36) =(1)/(6)`
(v) Number of favourable outcomes when
Sum of numbers on two dice is 6,i.e., (3,3),(3,3),(4,2),(4,2),(5,1),(5,1).
`therefore " "F(E) = 6`
` rArr " "P_(5) (E) = (F(E))/(T(E)) = (6)/(36) =(1)/(6)`
(vi) Number of favourable outcomes when
Sum of numbers on two dice is 7, i.e, (4,3),(4,3),(6,1),(6,1),(5,2) ,(5,2)`
`therefore " "F(E) = 6`
` rArr " "P_(6 ) (E) = (F(E))/(T(E)) = (6)/(36) =(1)/(6)`
(vii) Number of favourable outcomes when
Sum of numbers on two dice is 8 ,i.e., (5,3),(5,3),(6,2),(6 ,2).
`therefore " "F(E) = 6`
` rArr " "P_(7 ) (E) = (F(E))/(T(E)) = (6)/(36) =(1)/(6)`
(viii)Number of favourable outcoes when
Sum of numbers on both dice is 9 .i.e., (6,3),(6,3)
`therefore " "F(E) = 2`
`rArr " "P_(8)(E)=(F(E))/(T(E)) = (2)/(36) = (1)/(8)`