document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=317403>Question 317403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Market research in a particular city indicated that during a week 18% of all adults watch a television program oriented to business and financial issues, 12 % read a publication oriented to these issues and 10 % do both .\r<BR>\n" );
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document.write( "a) What is the probability that the adults fall at least one of these two groups ?<BR>\n" );
document.write( "b) What is the probability that an adult in the city who watches a television program oriented to business and financial issues reads a publication oriented to these issues ?<BR>\n" );
document.write( "c) Are the two events are statistically independent ? prove your answer . \r<BR>\n" );
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document.write( "Thank you .   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #227288 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=227288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Market research in a particular city indicated that during a week 18% of all adults watch a television program oriented to business and financial issues, <BR>\n" );
document.write( "12 % read a publication oriented to these issues and 10 % do both .<BR>\n" );
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document.write( "a) What is the probability that the adults fall are in at least one of these two groups ?<BR>\n" );
document.write( "P(tv or rd) = P(tv)+P(rd)-P(tv and rd) = 18+12-10 = 20%<BR>\n" );
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document.write( "b) What is the probability that an adult in the city who watches a television program oriented to business and financial issues reads a publication oriented to these issues ?<BR>\n" );
document.write( "P(rd |tv) = (rd and tv)/P(tv) = 0.10/0.18 = 0.56<BR>\n" );
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document.write( "c) Are the two events are statistically independent ? prove your answer<BR>\n" );
document.write( "Independent if P(rd | tv) = P(rd)<BR>\n" );
document.write( "But P(rd | tv) = 0.56<BR>\n" );
document.write( "and P(rd) = 0.12<BR>\n" );
document.write( "Therefore rd and tv are not independent.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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