A fair dice is rolled three times Let x the sum of the nume

A fair dice is rolled three times. Let x = the sum of the numerals resulting. Find as a fraction with denominator 6^2. Pr (chi = 6)

Solution

when a die of four face is rolled thrice then sample space is n(s) = 4³ = 64

A sum of 6 is obtained when {1,2,3},{2,3,1},{3,1,2},{1,3,2}{2,1,3}{3,2,1}{2,2,2}{1,1,4}{1,4,1}{4,1,1} n(A)=10.

p(A) = n(A) / n(S) = 10/64 = 5/32.