document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=923983>Question 923983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose 9 mice are available for a study of a possible carcinogen and 4 of themwill form a control group (i.e. will not receive the substance). Assuming that a random sample of 4 mice are selected, what is the probability that a particular mouse, Mike Mouse will be included in the control group? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560580 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=560580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A8%2A7%2A6%2F%281%2A2%2A3%2A4%29=126 ALIGN=MIDDLE  ALT=\"9%2A8%2A7%2A6%2F%281%2A2%2A3%2A4%29=126\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible groups of 4 mice.<BR>\n" );
document.write( "Some of those include Mike Mouse.<BR>\n" );
document.write( "How many groups of 4 mice including Mike Mouse are there?<BR>\n" );
document.write( "As many as groups of 3 mice made from the other eight mice.<BR>\n" );
document.write( "That is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2A6%2F%281%2A2%2A3%29=56 ALIGN=MIDDLE  ALT=\"8%2A7%2A6%2F%281%2A2%2A3%29=56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Of the total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126 ALIGN=MIDDLE  ALT=\"126\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible groups of 4 mice,<BR>\n" );
document.write( "there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56 ALIGN=MIDDLE  ALT=\"56\"   DISABLED_style= \"max-width:90%; height:auto;\" > such groups including Mike Mouse.<BR>\n" );
document.write( "The probability that Mike mouse will be included is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56%2F126=highlight%284%2F9=%220.4444...%22=%2244%25%28rounded%29%22%29 ALIGN=MIDDLE  ALT=\"56%2F126=highlight%284%2F9=%220.4444...%22=%2244%25%28rounded%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "A different way:<BR>\n" );
document.write( "As you select the first mouse,<BR>\n" );
document.write( "the probability of not selecting Mike Mouse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F9 ALIGN=MIDDLE  ALT=\"8%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that, the probability of not picking Mike as your second Mouse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F8 ALIGN=MIDDLE  ALT=\"7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that, the probability of not picking Mike as your third Mouse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F7 ALIGN=MIDDLE  ALT=\"6%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "And, if you have not picked Mike Mouse as one of the first 3 mice you pick,<BR>\n" );
document.write( "the probability of not picking Mike as your fourth Mouse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "All in all, the probability of not picking Mike Mouse as one of you four control mice is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F9%29%2A%287%2F8%29%2A%286%2F7%29%2A%285%2F6%29=8%2A7%2A6%2A5%2F%289%2A8%2A7%2A6%29=cross%288%29%2Across%287%29%2Across%286%29%2A5%2F%289%2Across%288%29%2Across%287%29%2Across%286%29%29=5%2F9 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So the probability of that not happening, and having Mike in your control group is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-5%2F9=highlight%284%2F9%29 ALIGN=MIDDLE  ALT=\"1-5%2F9=highlight%284%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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