A has a 2 in 12 chance of being at an end and a 10 in 12 chance of being somewhere in the middle. For the end seats, B has a 1 in 11 chance of sitting next to A, and a 2 in 11 chance of being next to A if A's in a non-end seat.
(2/12)*(1/11)+(10/12)*(2/11)=2/132+20/132=22/132 chance of being next to each other.
