The full backup will also contain the uncommitted transactions from transaction 4 at the time that the backup finishes. If a restore is necessary, the UNDO portion of the restore will roll back those transactions. Therefore, the full backup will contain transactions from all four of the transactions.
A small error in the question: transaction 1 never is committed, and transaction 2 is committed twice (which can't happen). Obviously, one of those transaction 2 commits is for transaction 1.
Edit: see http://technet.microsoft.com/en-us/magazine/2009.02.logging.aspx for more about the UNDO portion of recovery.