First, create a grouping query on Child that groups by SSN with a count of the number of records (count of year). I'll call that query qgrpYearsParticipated.
Create a second query where the Parent and Child tables are linked by the SSN and theremust be a match in both tables and the year column in Child must equal 2002, and also include the qgrpYearsParticipated linked (only records that are in both the Child table and the query) by SSN with the criteria of Count = 1.
The result will bethat the first part of the second query only lists matching records where the people participated in 2002. The second part only selects people who participated for one year, so since we're only displaying people who participated in 2002, if they only participated in one year then they are the ones who meet your criteria.