document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137840>Question 1137840</A>: <I><SPAN STYLE=\"word-break: break-all;\">        Suppose that an investor intends to buy stock in two companies.  He has narrowed his<BR>\n" );
document.write( "       interest to 5 stocks -- 3 industrials ( I1 , I2 , I3 ) and 2 utilities ( U1 , U2 ).  Suppose the<BR>\n" );
document.write( "       investor chooses 2 of these 5 stocks at random.  (Note:  They must be different stocks! <BR>\n" );
document.write( "       For example, I1 and I2 are different stocks as are I1 and U1.)\r<BR>\n" );
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document.write( "(a)	Display the sample space (S) of equally likely outcomes.  [Note that the order in<BR>\n" );
document.write( "       which the two stocks are chosen is not important.  So if ( I2, U1 ) are chosen, that is<BR>\n" );
document.write( "       the same as selecting ( U1, I2 ) ].  <BR>\n" );
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document.write( "     (b)  Let event A = the investor chooses 2 industrial stocks.  Find P(A).    <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755725 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52778)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Shortly saying,\r<BR>\n" );
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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( "(a)  the sample space is the space of all subsets of the given set, consisting of 2 elements,  or, in other words,\r\n" );
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document.write( "     The sample space is the set of all pairs (X,Y), where X and Y are different names from the given list of companies.\r\n" );
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document.write( "     In combinatorics, such type of sets is calling \"combinations of 5 names of the companies taken 2 at a time\".\r\n" );
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document.write( "     The number of elements in the sample space is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B3%2B2%5D%5E2 ALIGN=MIDDLE  ALT=\"C%5B3%2B2%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B5%5D%5E2 ALIGN=MIDDLE  ALT=\"C%5B5%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%29%2F%281%2A2%29 ALIGN=MIDDLE  ALT=\"%285%2A4%29%2F%281%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10.\r\n" );
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document.write( "(b)  Investor can select 2 of the 3 industrial stokes by  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B3%5D%5E2 ALIGN=MIDDLE  ALT=\"C%5B3%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A2%29%2F%281%2A2%29 ALIGN=MIDDLE  ALT=\"%283%2A2%29%2F%281%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2 ALIGN=MIDDLE  ALT=\"6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3 ways.\r\n" );
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document.write( "     So the probability of event A under question (B)  is  P(A) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F10 ALIGN=MIDDLE  ALT=\"3%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.3.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "On Combinations, &nbsp;see introductory lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Combinatorics: Combinations and permutations</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( "This my post is not to argue with the solution by Jim Thompson, which is absolutely correct.\r<BR>\n" );
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document.write( "It is to get you familiar with the terminology and key conceptions of Combinatorics, that are adjacent to this Probability problem.\r<BR>\n" );
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