document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187228>Question 187228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> /the probability that a married man watches a certain TV show is 0,4and the probability taht a married mwoman watches the show is 0.5.  The probability that a man watches the show agiven that his wife watches it is 0.7.  Find the probabiltiyt that a married couple watches the show; a wife watches the show given that her husband does; and at least one person of a married c ouple will watch the show.\r<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 #140363 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=140363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability that a married man watches a certain TV show is 0.4 <BR>\n" );
document.write( "and the probability that a married woman watches the show is 0.5. <BR>\n" );
document.write( "The probability that a man watches the show given that his wife watches is 0.7<BR>\n" );
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document.write( "Find the probability that a married couple watches the show; <BR>\n" );
document.write( "P(man AND woman) = P(man|woman)*P(woman) = 0.7*0.5 = 0.35<BR>\n" );
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document.write( "a wife watches the show given that her husband does; <BR>\n" );
document.write( "P(woman|man) = P(man AND woman)/P(man) = 0.35/0.4 = 0.8750<BR>\n" );
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document.write( "and at least one person of a married couple will watch the show.<BR>\n" );
document.write( "P(at least 1) = 1 - P(neither)<BR>\n" );
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document.write( "Need to figure out P(neither watch):<BR>\n" );
document.write( "P(both watch) = 0.35<BR>\n" );
document.write( "P(man watches and woman does not) = 0.40-0.35 = 0.05<BR>\n" );
document.write( "P(woman watches and man does not) = 0.50-0.35 = 0.15<BR>\n" );
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document.write( "P(neither watches) = 0.35+0.15+0.05 = 0.55<BR>\n" );
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document.write( "Therefore P(at least 1 watches) = 1 - 0.55 = 0.45<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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