document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=860804>Question 860804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #13<BR>\n" );
document.write( " A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories:<BR>\n" );
document.write( " A: Smooth <BR>\n" );
document.write( "B: Rhythm <BR>\n" );
document.write( "C: Standard <BR>\n" );
document.write( "The results were then presented to the owner in the following Venn Diagram. <BR>\n" );
document.write( "14 is Smooth ONLY (NOT RHYTHM, NOT STANDARD)<BR>\n" );
document.write( "31 is Rhythm ONLY (NOT SMOOTH, NOT STANDARD)<BR>\n" );
document.write( "30 is Standard ONLY (NOT SMOOTH, NOT RHYTHM)<BR>\n" );
document.write( "44 is Smooth and Rhythm ONLY (NOT STANDARD)<BR>\n" );
document.write( "18 is Smooth and Standard ONLY (NOT RHYTHM)<BR>\n" );
document.write( "39 is Rhythm and Standard ONLY (NOT SMOOTH)<BR>\n" );
document.write( "11 is Smooth,Rhythm,Standard ALL THREE<BR>\n" );
document.write( "48 is none <BR>\n" );
document.write( "If a student is chosen at random, what is the probability that: <BR>\n" );
document.write( "Round all answers to 3 decimal places as needed. <BR>\n" );
document.write( "A student has competed in none of the categories? is it .256684442? \r<BR>\n" );
document.write( "\n" );
document.write( "A student has competed in Smooth, Rhythm, or Standard? is it .4010695187? \r<BR>\n" );
document.write( "\n" );
document.write( "A student has competed in Smooth or Standard, but not Rhythm? Is it .0695187166?<BR>\n" );
document.write( " <BR>\n" );
document.write( "A student has competed in Rhythm and Standard, but not Smooth? Is it .2517368984?<BR>\n" );
document.write( " <BR>\n" );
document.write( "A student has competed in Rhythm, given you know they have competed in Smooth. Is it .2406417112?<BR>\n" );
document.write( " #14<BR>\n" );
document.write( " A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories:<BR>\n" );
document.write( " A: Smooth <BR>\n" );
document.write( "B: Rhythm <BR>\n" );
document.write( "C: Standard <BR>\n" );
document.write( "The results were then presented to the owner in the following Venn Diagram. <BR>\n" );
document.write( "46 is Smooth <BR>\n" );
document.write( "36 is Rhythm <BR>\n" );
document.write( "11 is Standard <BR>\n" );
document.write( "40 is Smooth and Rhythm <BR>\n" );
document.write( "22 is Smooth and Standard <BR>\n" );
document.write( "16 is Rhythm and Standard <BR>\n" );
document.write( "47 is Smooth,Rhythm and Standard <BR>\n" );
document.write( "17 is none\r<BR>\n" );
document.write( "\n" );
document.write( " If a student is chosen at random, what is the probability that: <BR>\n" );
document.write( "Round all answers to 3 decimal places as needed. <BR>\n" );
document.write( "A student has competed in none of the categories? Is it .0779816514? \r<BR>\n" );
document.write( "\n" );
document.write( "A student has competed in Smooth, Rhythm, or Standard? Is it .4266055046? \r<BR>\n" );
document.write( "\n" );
document.write( "A student has competed in Smooth or Standard, but not Rhythm? Is it .0963302752?<BR>\n" );
document.write( " <BR>\n" );
document.write( "A student has competed in Rhythm and Standard, but not Smooth? -.0871559633? \r<BR>\n" );
document.write( "\n" );
document.write( "A student has competed in Rhythm, given you know they have competed in Smooth. Is it .376146789?<BR>\n" );
document.write( " I COULD NOT PUT IN THE VENN DIAGAM ON HERE FOR BOTH. NEED IT BY APRIL 8TH BY 11:59PM THANK YOU I only get three tries on before problems and these if i get it wrong new problem. ok thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #518687 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=518687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Notice I have put in the \"ONLY\"'s below.  Otherwise it wouldn't make\r\n" );
document.write( "sense to have, for instance, 44 as both smooth and rhythm but only 14 \r\n" );
document.write( "as smooth.  The 44 that are both smooth and rhythm are \r\n" );
document.write( "also part of the smooth set.  So I will assume you mean the Venn\r\n" );
document.write( "diagram below.  Realize this about the overlapping three circles:\r\n" );
document.write( "\r\n" );
document.write( "The upper left circle is the SMOOTH circle. It contains 14+44+11+18 = 87\r\n" );
document.write( "The upper right circle is the RHYTHM circle. It contains 44+31+39+11 = 125\r\n" );
document.write( "The lower circle is the STANDARD circle.  It contains 18+11+39+30 = 98\r\n" );
document.write( "\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories:<BR>\n" );
document.write( "A: Smooth <BR>\n" );
document.write( "B: Rhythm <BR>\n" );
document.write( "C: Standard <BR>\n" );
document.write( "The results were then presented to the owner in the following Venn Diagram. <BR>\n" );
document.write( "14 is Smooth ONLY (NOT RHYTHM, NOT STANDARD)<BR>\n" );
document.write( "31 is Rhythm ONLY (NOT SMOOTH, NOT STANDARD)<BR>\n" );
document.write( "30 is Standard ONLY (NOT SMOOTH, NOT RHYTHM)<BR>\n" );
document.write( "44 is Smooth and Rhythm ONLY (NOT STANDARD)<BR>\n" );
document.write( "18 is Smooth and Standard ONLY (NOT RHYTHM)<BR>\n" );
document.write( "39 is Rhythm and Standard ONLY (NOT SMOOTH)<BR>\n" );
document.write( "11 is Smooth,Rhythm,Standard (ALL THREE)<BR>\n" );
document.write( "48 is none <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C4%2C-5%2C4%2C%0D%0Arectangle%28-4%2C-3.5%2C4%2C4%29%2C%0D%0Acircle%280%2C-.5%2C2%29%2C%0D%0Alocate%28-2%2C2%2C14%29%2C%0D%0Alocate%28-3.5%2C-2%2C48%29%0D%0Alocate%280%2C-2.7%2CC%28STANDARD%29%29%2C%0D%0Alocate%28-.3%2C-1%2C30%29%2C%0D%0Alocate%281.1%2C.4%2C39%29%2C+%0D%0Acircle%28sqrt%282%29%2Csqrt%282%29%2C2%29%2C+%0D%0Alocate%28-3.5%2C4%2CA%28SMOOTH%29%29%2C%0D%0Acircle%28-sqrt%282%29%2Csqrt%282%29%2C2%29%2C%0D%0Alocate%281.5%2C4%2CB%28RHYTHM%29%29%2C%0D%0Alocate%28-1.3%2C.5%2C18%29%2C%0D%0Alocate%28-.2%2C2.5%2C44%29%2C%0D%0Alocate%282%2C2%2C31%29%2C%0D%0Alocate%28-.2%2C1.1%2C11%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "\r\n" );
document.write( "Here are what the numbers mean:\r\n" );
document.write( "The 14 are SMMOTH, but NOT rhythm and NOT standard\r\n" );
document.write( "The 44 are SMOOTH and RHYTHM, but NOT standard\r\n" );
document.write( "The 31 are RHYTHM, but NOT smooth and not standard\r\n" );
document.write( "The 18 are SMOOTH and STANDARD, but NOT rhythm\r\n" );
document.write( "The 11 are SMOOTH, RHYTHM, and STANDARD. (They are inside ALL THREE CIRCLES)\r\n" );
document.write( "The 39 are RHYTHM and STANDARD, but not SMOOTH\r\n" );
document.write( "The 30 are STANDARD, but not smooth and not rhythm\r\n" );
document.write( "The 48 are neither smooth, rhythm, nor standard.\r\n" );
document.write( " \r\n" );
document.write( "Add all 8 numbers\r\n" );
document.write( "14+44+31+18+11+39+30+48 = 235 students in the survey.\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "If a student is chosen at random, what is the probability that: <BR>\n" );
document.write( "--------------- <BR>\n" );
document.write( "A student has competed in none of the categories? is it .256684442? <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "No it's not. It's the 48 that are outside all three circles -- out \r\n" );
document.write( "of the 235 total, which is the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2F235 ALIGN=MIDDLE  ALT=\"48%2F235\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .2042553191  \r\n" );
document.write( "</PRE><BR>\n" );
document.write( "A student has competed in Smooth, Rhythm, or Standard? is it .4010695187?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "No it's not. It's all of the 14+44+31+18+11+39+30 = 187 that are in one\r\n" );
document.write( "of the circles -- out of the 235 total, which is the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=187%2F235 ALIGN=MIDDLE  ALT=\"187%2F235\"   DISABLED_style= \"max-width:90%; height:auto;\" > =\r\n" );
document.write( ".7957446809.  (You could also get 187 just by subtracting the 48, that are not\r\n" );
document.write( "in any of the circles, from the 235.)  \r\n" );
document.write( "</PRE><BR>\n" );
document.write( "A student has competed in Smooth or Standard, but not Rhythm? Is it .0695187166?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "No it's not.  It's the 14+18+30=62 that are in inside either the SMOOTH or\r\n" );
document.write( "the standard circle but outside the Rhythm circle  -- out of the 235 total, which is the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=62%2F235 ALIGN=MIDDLE  ALT=\"62%2F235\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .2638297872.\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "A student has competed in Rhythm and Standard, but not Smooth? Is it .2517368984?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "No it's not.  It's the 31+39+30=100 that are inside either the Rhythm or \r\n" );
document.write( "the Standard circle but outside the Smooth circle  -- out of the 235 total, which is the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F235 ALIGN=MIDDLE  ALT=\"100%2F235\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .4255319149.\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "A student has competed in Rhythm, given you know the student has competed in<BR>\n" );
document.write( "Smooth. Is it .2406417112?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "No it's not.  We are given that the student is one of the 18+11+39+30=98 which\r\n" );
document.write( "are inside the Smooth Circle.  So the probability that the student is also\r\n" );
document.write( "inside the Rhythm circle, is that he or she is one of 11+44=55 students that\r\n" );
document.write( "are inside both the Smooth and Rhythm circles.\r\n" );
document.write( "\r\n" );
document.write( "Answer: 55 out of the 98 or the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2F98 ALIGN=MIDDLE  ALT=\"55%2F98\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .5612244898.\r\n" );
document.write( "\r\n" );
document.write( "Now hopefully, you'll study this one and learn how a Venn diagram of three\r\n" );
document.write( "overlapping circles work, and learn what each of the 8 regions mean, and be\r\n" );
document.write( "able to do the other one on your own.   If you have any questions, ask them\r\n" );
document.write( "in the thank-you note and I'll get back to you by email, and I'll help you\r\n" );
document.write( "with the other one.  No charge, I just do this for fun.\r\n" );
document.write( "\r\n" );
document.write( "Edwin</PRE> </SPAN>\n" );
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