document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867943>Question 867943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having trouble with this problem. I get parts of it but can't seem to understand what the total variable is. Here is the problem:<BR>\n" );
document.write( "A town has an ice cream shop, a bowling alley, and a park. Students hang out at one of these 3 places on a Friday night. A given student re-evaluates the choice to be at a particular location every 10 minutes as follow:<BR>\n" );
document.write( "1. If at the park, the student goes to the bowling alley 10% of the time, the ice cream shop 20% of the time, and the otherwise stays put.<BR>\n" );
document.write( "2. If at the bowling alley, the student goes to the park 5% of the time, to the ice cream shop 10% of the time, and otherwise stays put.<BR>\n" );
document.write( "3. If at the ice cream shop, the student goes to the park 35% of the time, to the bowling alley 15% of the time, and otherwise stays put. \r<BR>\n" );
document.write( "\n" );
document.write( "The police drive by the park and tell the students there to go home. Estimate the fraction of students that was told to go home, (from the park). \r<BR>\n" );
document.write( "\n" );
document.write( "I get what percentage of the time for each occasion the student goes to the park, but how can I make this into a formula so that I can solve it when each occasion is conditional and there is no clear total variable given. Any help with this will be greatly appreciated. Thank you very much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #525934 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=525934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's start with 100 in each place<BR>\n" );
document.write( "b(1)=100 i(1)=100 p(1)=100<BR>\n" );
document.write( "1)b(2)=b(1)+.10*p(1) <BR>\n" );
document.write( "1)i(2)=i(1)+.20*p(1)<BR>\n" );
document.write( "1)p(2)=.70*p(1)<BR>\n" );
document.write( "2)p(2)=p(2)+.05*b(1)<BR>\n" );
document.write( "2)i(2)=i(2)+.10*b(1)<BR>\n" );
document.write( "2)b(2)=.85*b(1)<BR>\n" );
document.write( "3)p(2)=p(2)+.35*i(1)<BR>\n" );
document.write( "3)b(2)=b(2)+.15*i(1)<BR>\n" );
document.write( "3)i(2)=.50*i(1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0)b(1)=100<BR>\n" );
document.write( "2)b(2)=.85*b(1)<BR>\n" );
document.write( "1)b(2)=b(1)+.10*p(1) <BR>\n" );
document.write( "3)b(2)=b(2)+.15*i(1)<BR>\n" );
document.write( "85+15+10=110<BR>\n" );
document.write( "i's<BR>\n" );
document.write( "0)i(1)=100 <BR>\n" );
document.write( "3)i(2)=.50*i(1)<BR>\n" );
document.write( "1)i(2)=i(1)+.20*p(1)<BR>\n" );
document.write( "2)i(2)=i(2)+.10*b(1)\r<BR>\n" );
document.write( "\n" );
document.write( "50+20+10=80<BR>\n" );
document.write( "p's<BR>\n" );
document.write( "0)p(1)=100<BR>\n" );
document.write( "1)p(2)=.70*p(1)<BR>\n" );
document.write( "2)p(2)=p(2)+.05*b(1)<BR>\n" );
document.write( "3)p(2)=p(2)+.35*i(1)<BR>\n" );
document.write( "70+5+35=110<BR>\n" );
document.write( "We are only interested in p<BR>\n" );
document.write( "110  in the park after 10 minutes </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );