document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866140>Question 866140</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A family has 4 children. Using a tree diagram that shows how many ways the children could have been born, from first to last born, determine how many ways the family could have had 2 boys and 2 girls. Then find the probability of having 2 boys and 2 girls. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522104 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=522104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a tree diagram depicting all the possible ways to have 4 kids\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" width = \"500\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/tree_zps53b06649.png\">\r<BR>\n" );
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document.write( "The first column (of just 2 choices) represents child #1. \r<BR>\n" );
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document.write( "If we stop at the second column, and ignore everything past it, then we see that there are 2^2 = 4 ways to have 2 kids (and those ways are shown in the tree diagram)\r<BR>\n" );
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document.write( "Likewise, if we stop at column #3, then we see all the possible ways to have 3 kids (2^3 = 8 different ways)\r<BR>\n" );
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document.write( "The last column is that last and 4th child. There are 2^4 = 16 ways to have 4 kids. Each possible path you trace (from the starting node to either a B or G in the fourth column) generates a sequence of 4 letters (either B or G) that represents a combination of boys and/or girls. For example, trace along the very top branches and you'll only pick up B, B, B, B or BBBB which represents all 4 kids being boys.\r<BR>\n" );
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document.write( "Let's highlight all of the paths that have exactly 2 boys and exactly 2 girls.\r<BR>\n" );
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document.write( "Here is one path\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" width = \"500\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/bbgg_zps281a6be4.png\">\r<BR>\n" );
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document.write( "This is the sequence BBGG which means the first two kids are boys, the second 2 are girls (boy, boy, girl, girl)\r<BR>\n" );
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document.write( "Here is another\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" width = \"500\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/bgbg_zps1e2982bd.png\">\r<BR>\n" );
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document.write( "That is the sequence BGBG (boy, girl, boy, girl)\r<BR>\n" );
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document.write( "Here is another\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" width = \"500\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/bggb_zps368ee9bc.png\">\r<BR>\n" );
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document.write( "This sequence is BGGB (boy, girl, girl, boy)\r<BR>\n" );
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document.write( "and here is another path of exactly 2 girls, 2 boys\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" width = \"500\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/gbbg_zps7d735261.png\">\r<BR>\n" );
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document.write( "This sequence is GBBG (girl, boy, boy, girl)\r<BR>\n" );
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document.write( "and here is another path of exactly 2 girls, 2 boys\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" width = \"500\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/gbgb_zpsa66f5211.png\">\r<BR>\n" );
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document.write( "This sequence is GBGB (girl, boy, girl, boy)\r<BR>\n" );
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document.write( "and finally, here is the last path that represents exactly 2 girls, 2 boys\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" width = \"500\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/ggbb_zpsdad0dca2.png\">\r<BR>\n" );
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document.write( "This sequence is GGBB (girl, girl, boy, boy)\r<BR>\n" );
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document.write( "There are 6 sequences highlighted above and they are\r<BR>\n" );
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document.write( "BBGG<BR>\n" );
document.write( "BGBG <BR>\n" );
document.write( "BGGB <BR>\n" );
document.write( "GBBG <BR>\n" );
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document.write( "GGBB\r<BR>\n" );
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document.write( "So there are <font color=\"red\">6</font> ways to have 2 boys and 2 girls (they are shown above).\r<BR>\n" );
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document.write( "To calculate the probability of having 2 boys and 2 girls, you divide that last number we found (6) by 16. This is because there are 16 ways to have 4 kids (2^4 = 16)\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F16+=+3%2F8 ALIGN=MIDDLE  ALT=\"6%2F16+=+3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The answer as a fraction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now use a calculator to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8+=+0.375 ALIGN=MIDDLE  ALT=\"3%2F8+=+0.375\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The answer as a decimal is <font color=\"red\">0.375</font>\r<BR>\n" );
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document.write( "And multiply that decimal result by 100 to convert it over to a percentage 0.375*100 = 37.5%\r<BR>\n" );
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document.write( "The answer as a percentage is <font color=\"red\">37.5%</font> </SPAN>\n" );
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