Assume every person to be vertex and no of sibling be the degree of vertex
so the degree sequence will be {1,1,1,1,2,2,2} for the vertices let's say {A,B,C,D,E,F,G}
one of the graphs possible is A is the sibling of B and vice versa(there exists edge between A and B ), C is the sibling of D and vice versa (there exists edge between C and D), E, F, and G are siblings of each other(there exists edge between every possible pair of E,F and G).
P(selecting a pair of persons which are siblings)=( C(2,2)(for the A and B case)+C(2,2)(for the C and D case)+C(3,2)(for the E,F and G case))/C(7,2)(for all possible pairs)
=(1+1+3)/21 = 5/21
required probability = 1-(5/21)=16/21