Official solution
Out of 11 consecutive natural numbers either
6 even and 5 odd numbers or 5 even and 6
odd numbers.
Let, E = Even
O = Odd
Case-1 :
E, O, E, O, E, O, E, O, E, O, E
2b = a + c \[ \Rightarrow \] Even
\[ \Rightarrow \] Both a and c should be either even or odd.
P = \[{{{}^6{C_2} + {}^5{C_2}} \over {{}^{11}{C_3}}}\] = \[{5 \over {33}}\]
Case -2 :
O, E, O, E, O, E, O, E, O, E, O
P = \[{{{}^5{C_2} + {}^6{C_2}} \over {{}^{11}{C_3}}}\] = \[{5 \over {33}}\]
Total probability = \[{1 \over 2} \times {5 \over {33}}\] + \[{1 \over 2} \times {5 \over {33}}\] = \[{5 \over {33}}\]