document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266331>Question 266331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The medal distribution from the 2004 Summer Olympic Games for the top 23 countries is shown below:\r<BR>\n" );
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document.write( "                Gold   Silver  Bronze<BR>\n" );
document.write( "U.S.            35     39      29<BR>\n" );
document.write( "Russia          27     27      38<BR>\n" );
document.write( "China           32     17      14<BR>\n" );
document.write( "Australia       17     16      16<BR>\n" );
document.write( "Others         133    136     153\r<BR>\n" );
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document.write( "Choose 1 medal winner at random.<BR>\n" );
document.write( "a. Find the probability that the winner won the gold medal, given that the winner was from the U.S.\r<BR>\n" );
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document.write( "b. Find the probability that the winner was from the U.S. given that she or he won a gold medal.\r<BR>\n" );
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document.write( "c. Are the events \"medal winner is from U.S.\" and \"gold medal won\" independent? Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195869 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=195869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The medal distribution from the 2004 Summer Olympic Games for the top 23 countries is shown below:\r<BR>\n" );
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document.write( "                Gold   Silver  Bronze Total<BR>\n" );
document.write( "U.S.            35     39      29       104<BR>\n" );
document.write( "Russia          27     27      38        92<BR>\n" );
document.write( "China           32     17      14        63<BR>\n" );
document.write( "Australia       17     16      16        49<BR>\n" );
document.write( "Others         133    136     153       422<BR>\n" );
document.write( "----------------------------------------730<BR>\n" );
document.write( "Choose 1 medal winner at random.<BR>\n" );
document.write( "a. Find the probability that the winner won the gold medal, given that the winner was from the U.S.<BR>\n" );
document.write( "P(gold|US win) = P(gold and US)/P(uS win) = 35/104<BR>\n" );
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document.write( "b. Find the probability that the winner was from the U.S. given that she or he won a gold medal.<BR>\n" );
document.write( "Prob = 35/133<BR>\n" );
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document.write( "c. Are the events \"medal winner is from U.S.\" and \"gold medal won\" independent? Explain.<BR>\n" );
document.write( "Check to see if P(A|B) = P(A)*P(B)<BR>\n" );
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document.write( "P(from U.S.| gold won) = P(from U.S. AND gold won)/P(gold won)<BR>\n" );
document.write( "= (35/730)/(133/730) = 35/730<BR>\n" );
document.write( "P(from U.S.)*P(gold won) = (104/730)(133/730)<BR>\n" );
document.write( "Ans: The results are not equal so the factors are no independent.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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