Answer:
A. Smith pays a carpenter $50,000 to build a garage.  ⇒ INCLUDED, increases GDP by $50,000 because Smith paid for the garage. 
B. Smith purchases $10,000 worth of materials and builds a garage, which is worth $50,000.  ⇒ INCLUDED, increases GDP by $10,000 only because Smith built the garage himself. 
C. Smith goes to the woods, cut down a tree, and uses the wood to build himself a garage that is worth $50,000.  ⇒ NOT INCLUDED, no services or goods were exchanged, it is the same as growing your own food. 
D. The Jones family sells its old house to the Reynolds family for $400,000. The Joneses then buy a newly constructed house from a builder for $500,000.  ⇒ INCLUDED, increases GDP by $500,000 because the Joneses purchased anew house. 
E. You purchase a used computer from a friend for $200.  ⇒ NOT INCLUDED, only new goods and services are included. 
F. Your university purchases a new mainframe computer from IBM, paying $25,000.   ⇒ INCLUDED, increases GDP by $25,000 because the university purchased a new computer.
G. You win $100 in an Atlantic City casino. ⇒ NOT INCLUDED, casino earnings or lottery earnings are not considered new products or services.