Why does every year contain at least one Friday the 13th and not more than three?

Yes. It occurs at least once every year (in fact, about/appx. every eight months). For example:

1993 - August

1994 - May

1995 - January & October

1996 - September & December

1997 - June

1998 - February, March & November

1999 - August

2000 - October

2001 - April & July

2002 - September & December

2003 - June

2004 - February & August

2005 - May

2006 - January & October

2007 - April & July

2008 - June

This is incorrect. Friday the 13th is on May 13, 2011, and the next occurance happens on January 13th, 2012.