Final answer:
The probability that a particular pair of people are seated next to each other around a circular table is 2/9.
Step-by-step explanation:
The probability that a particular pair of people are seated next to each other around a circular table can be calculated by considering the total number of possible arrangements and the number of favorable arrangements.
There are 10 people, so there are 10 possible seats for the first person. Once the first person is seated, there are 9 possible seats remaining for the second person. However, if the pair must be seated next to each other, the second person can only be seated next to the first person in one of two seats (either to the left or right). So the probability is 2/9.