Dale un vistazo al API de Java la respuesta es muy sencilla:
Cita: public FileOutputStream(File file,
boolean append)
throws FileNotFoundException
Creates a file output stream to write to the file represented by the specified File object. If the second argument is true, then bytes will be written to the end of the file rather than the beginning. A new FileDescriptor object is created to represent this file connection.
First, if there is a security manager, its checkWrite method is called with the path represented by the file argument as its argument.
If the file exists but is a directory rather than a regular file, does not exist but cannot be created, or cannot be opened for any other reason then a FileNotFoundException is thrown.
Parameters:
file - the file to be opened for writing.
append - if true, then bytes will be written to the end of the file rather than the beginning
Throws:
FileNotFoundException - if the file exists but is a directory rather than a regular file, does not exist but cannot be created, or cannot be opened for any other reason
SecurityException - if a security manager exists and its checkWrite method denies write access to the file.
Since:
1.4
See Also:
File.getPath(), SecurityException, SecurityManager.checkWrite(java.lang.String)
Traducido... cambia tu codigo por:
new ObjectOutputStream(new FileOutputStream("tasques.txt",true));