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" );
document.write( "     <BR>\n" );
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 #755720 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=755720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "Part A\r<BR>\n" );
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document.write( "Make a table that looks something like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/vTVypk6.png\"><BR>\n" );
document.write( "The stuff in red along the rows is the first stock picked while the stuff in blue along the columns is the second stock picked. <BR>\n" );
document.write( "Each cell in the form (x,y) is a result of picking one of each color. \r<BR>\n" );
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document.write( "Eg: row 2, column 4 has (I2, U1) in it from red I2 along the left hand side and the blue U1 up top. You can think of it as a game of battleship in terms of how you locate a ship you want to target.\r<BR>\n" );
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document.write( "Mark out the main diagonal. I'm doing so in yellow highlighter<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/zNFrylY.png\"><BR>\n" );
document.write( "This main diagonal is where you pick the same stock twice. This isn't possible, so we will ignore this diagonal and anything below it (the stuff below the diagonal is a symmetric copy of the stuff above the diagonal). The cells we ignore can be blotted out like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/sbXXOCR.png\"><BR>\n" );
document.write( "The stuff that isn't covered up forms the sample space\r<BR>\n" );
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document.write( "S = sample space \r\n" );
document.write( "S = set of all possible ways to pick 2 stocks\r\n" );
document.write( "S = {(I1, I2),   (I1, I3),   (I1, U1),   (I1, U2),\r\n" );
document.write( "                 (I2, I3),   (I2, U1),   (I2, U2),\r\n" );
document.write( "                             (I3, U1),   (I3, U2),\r\n" );
document.write( "                                         (U1, U2) }\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "This formatting mimics the pattern in how the remaining ordered pairs show up in the table. Otherwise things could get a bit cluttered. The curly braces tell the reader \"this is a set\".\r<BR>\n" );
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document.write( "Extra info:<BR>\n" );
document.write( "There are 4 items in row 1<BR>\n" );
document.write( "There are 3 items in row 2<BR>\n" );
document.write( "There are 2 items in row 3<BR>\n" );
document.write( "There is 1 item in row 4<BR>\n" );
document.write( "In total, there are 4+3+2+1 = 10 items in the sample space.\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "A = event that investor picks two industrial stocks<BR>\n" );
document.write( "A = set of all pairs (x,y) such that x and y are picked from {I1,I2,I3}<BR>\n" );
document.write( "A = { (I1, I2),	(I1, I3), (I2, I3) }<BR>\n" );
document.write( "We can see this by highlighting these cells below<BR>\n" );
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document.write( "There are 3 ways to get what we want out of 10 items total (sample space size)\r<BR>\n" );
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document.write( "The answer as a fraction is 3/10</font> </SPAN>\n" );
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