document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203046>Question 203046</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If two numbers are randomly chosen without replacement from {1, 2, 3, 4, 5}, what is the probability their sum is greater than their product? Express your answer as a common fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #484463 by </B><A HREF=/tutors/aboutme.mpl?userid=albertemc><B>albertemc(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=albertemc><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=484463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sorry jsmall I'ma afraid your answer is wrong.\r<BR>\n" );
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document.write( "The question is asking : if 2 numbers are picked randomly WITHOUT REPLACEMENT. \r<BR>\n" );
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document.write( "hence, while you may use the multiplicative probability properties, the second probability of drawing a number that is not 1 is not 5/6  (further more , the student is asking about the numbers (1,2,3,4,5)  , 6 is not included\r<BR>\n" );
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document.write( "But lets assume we are dealing with (1,2,3,4,5,6) when you pick your first choice, you have 5/6 chance of picking numbers not 1, \r<BR>\n" );
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document.write( "namely, 2,3,4,5,6.\r<BR>\n" );
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document.write( "in your second choice, since you are drawing without replacement, you have only  5 options left, assumed you have picked 4 for your first choice, you now have 1,2,3,5,6 to choose from, however, you don't want to choose one, so you have 4/5 chance of picking numbers not 1.\r<BR>\n" );
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document.write( "hence, the probability of not drawing 2 numbers whose sum is greater than product is (5/6)*(4/5) = (4/6) = 2/3.\r<BR>\n" );
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document.write( "probability of drawing 2 numbers whose sum is greater than product is then 1/3\r<BR>\n" );
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document.write( "Alternatively, you may see that there are (6 choose 2) = 15 ways to pick 2 random numbers out of 6.  And there are 5 ways to choose 2 numbers such that 1 is included (1,2) (1,3) ..... (1,5). since the probability of drawing any two numbers are the same, therefore, 5/15 = 1/3 is the probability of drawing 2 numbers whose sum is greater than their product.\r<BR>\n" );
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document.write( "So I think you have all the tools you need to solve the problem with just (1,2,3,4,5) :) </SPAN>\n" );
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