Question

Six faces of a die are marked with numbers 1,-1,0,-2,2,3 and the die is thrown thrice. The probability that the sum of the numbers thrown is six, is A. 1 72 B. 1 12 C. 5 108 D. 1 36 Select the correct answer from above options

Answer 1

Correct Answer - C Total number of elementary events =63 . Favourable number of elementary events =Coeff.of x6 in (x+x-1+ 0 x +x-2+x2+x3)3 = Coeff.of x12 in ( 1+x+x2+x3+x4+x5 x2 )3 = Coeff.of x12 in (1+x+x2+x3+x4+x5)3 =Coeff. of x12 in ( 1-x6 1-x )3 = Coeff.of x12 in (1-x6)3(1-x)-3 =Coeff.of x12 in (1-.3C1x6+.3C2x12..)(1-x)-3 =Coeff.of x12 in (1-x)-3-.3C1× Coeff.ofx6 in (1-x)-3+.3C2× Coeff.ofx0 in (1-x)-3 x 12 in ( 1 − x ) − 3 − . 3 C 1 × Coeff.of x 6 in ( 1 − x ) − 3 + . 3 C 2 × Coeff.of x 0 in ( 1 − x ) − 3 =.12+3-1C3-1-.3C1×.6+3-1C3-1+.3C2 =.14C2-.3C1×.8C2+.3C2=91-84+3=10 . Hence, required probability = 10 63 = 5 108 .