In a performance of "Singing Revolutionary Songs" attended by six units including A and B, the programs of each unit are arranged together. If the lottery is adopted, it will be followed.

Solution: Considering the arrangement of unit A and unit B,

Units A and B can be arranged in any two of the six positions, and there are 30 possible results.

(1) Let A mean "The performance serial numbers of A and B are even",

Then a contains six results,

So the probability is P(A)= =.

(2) Let b represent "the performance serial numbers of unit A and unit B are not adjacent",

The serial numbers indicating A and B are adjacent and contain 10 results.

So P(B)= 1-P( )= 1- =.