document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047218>Question 1047218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help on this probability question.  I got 1/16 as an answer by multiplying (1/2)*(1/2)*(1/2)*(1/2) = 1/16 I am not sure if I am right.<BR>\n" );
document.write( "A couple decides to have 4 children.  If they succeed in having4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662726 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=662726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A%281%2F2%29%2A%281%2F2%29%2A%281%2F2%29+=+1%2F16 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A%281%2F2%29%2A%281%2F2%29%2A%281%2F2%29+=+1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is the probability that they will have<BR>\n" );
document.write( "girl, girl, girl, girl, in that order.<BR>\n" );
document.write( "It is also the probability of<BR>\n" );
document.write( "boy, boy, boy, boy, in that order,<BR>\n" );
document.write( "and it is the probability of any sequence of 4 children,<BR>\n" );
document.write( "such as<BR>\n" );
document.write( "boy, boy, girl, girl, or<BR>\n" );
document.write( "girl, girl, boy, boy, or<BR>\n" );
document.write( "boy, girl, boy, girl, or<BR>\n" );
document.write( "girl, boy, girl, boy, or<BR>\n" );
document.write( "boy, girl, girl, boy, or<BR>\n" );
document.write( "girl, boy, boy,girl.<BR>\n" );
document.write( "So out of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > sequences possible<BR>\n" );
document.write( "there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > sequences that would give them exactly 2 girls and 2 boys.<BR>\n" );
document.write( "The probability of that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F16=highlight%283%2F8=0.375=%2237.5%25%22%29 ALIGN=MIDDLE  ALT=\"6%2F16=highlight%283%2F8=0.375=%2237.5%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "When you are faced with problems of that sort,<BR>\n" );
document.write( "think of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28boy%2Bgirl%29%5E4 ALIGN=MIDDLE  ALT=\"%28boy%2Bgirl%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E4 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( "In the painful <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E4=%28a%2Bb%29%2A%28a%2Bb%29%2A%28a%2Bb%29%2A%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E4=%28a%2Bb%29%2A%28a%2Bb%29%2A%28a%2Bb%29%2A%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplication,<BR>\n" );
document.write( "you would end with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A2%2A2=2%5E4=16 ALIGN=MIDDLE  ALT=\"2%2A2%2A2%2A2=2%5E4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > products,<BR>\n" );
document.write( "including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%284%29 ALIGN=MIDDLE  ALT=\"red%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3b ALIGN=MIDDLE  ALT=\"a%5E3b\"   DISABLED_style= \"max-width:90%; height:auto;\" > product terms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%286%29 ALIGN=MIDDLE  ALT=\"green%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%284%29 ALIGN=MIDDLE  ALT=\"blue%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%5E3 ALIGN=MIDDLE  ALT=\"ab%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but then you \"collect like terms\" to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E4=a%5E4%2Bred%284%29a%5E3b%2Bgreen%286%29a%5E2b%5E2%2Bblue%284%29ab%5E3%2Bb%5E4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%286%29a%5E2b%5E2 ALIGN=MIDDLE  ALT=\"green%286%29a%5E2b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells you that there were <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%286%29 ALIGN=MIDDLE  ALT=\"green%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "outcomes where 2 a's and 2 b's happened, in various orders.<BR>\n" );
document.write( "The probability of that happening is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%286%29%2F16 ALIGN=MIDDLE  ALT=\"green%286%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );