document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=52671>Question 52671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small town has 5,600 residents.  The residents in the town were asked whether or not they favored building a new bridge across the river.  You are given the following information on the residents' responses, broken down by sex.			<BR>\n" );
document.write( "		Men	Women	Total<BR>\n" );
document.write( "In Favor	1,400	   280	1,680<BR>\n" );
document.write( "Opposed	   840	3,080	3,920<BR>\n" );
document.write( "Total	2,240	3,360	5,600\r<BR>\n" );
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document.write( "	 \r<BR>\n" );
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document.write( "	Let:	M be the event a resident is a man<BR>\n" );
document.write( "		W be the event a resident is a woman<BR>\n" );
document.write( "		F be the event a resident is in favor<BR>\n" );
document.write( "		P be the event a resident is opposed\r<BR>\n" );
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document.write( "	a.	Find the joint probability table.<BR>\n" );
document.write( "	b.	Find the marginal probabilities.<BR>\n" );
document.write( "	c.	What is the probability that a randomly selected resident is a man and is in favor of building the bridge?<BR>\n" );
document.write( "	d.	What is the probability that a randomly selected resident is a man?<BR>\n" );
document.write( "	e.	What is the probability that a randomly selected resident is in favor of building the bridge?<BR>\n" );
document.write( "	f.	What is the probability that a randomly selected resident is a man or in favor of building the bridge?<BR>\n" );
document.write( "	g.	A randomly selected resident turns out to be male.  Compute the probability that he is in favor of building the bridge.<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 #35520 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=35520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 		Men	Women	Total<BR>\n" );
document.write( "In Favor	1,400	   280	1,680<BR>\n" );
document.write( "Opposed	   840	3,080	3,920<BR>\n" );
document.write( "Total	2,240	3,360	5,600\r<BR>\n" );
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document.write( "	 \r<BR>\n" );
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document.write( "	Let:	M be the event a resident is a man<BR>\n" );
document.write( "		W be the event a resident is a woman<BR>\n" );
document.write( "		F be the event a resident is in favor<BR>\n" );
document.write( "		P be the event a resident is opposed\r<BR>\n" );
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document.write( "	a.	Find the joint probability table.<BR>\n" );
document.write( "Need figure prob of M&F, W&F, M&O, W&O<BR>\n" );
document.write( "For example P(M&F)=1400/5600=0.25<BR>\n" );
document.write( "	b.	Find the marginal probabilities.<BR>\n" );
document.write( "Nee figure Prob of M, of W, of F, or O<BR>\n" );
document.write( "For example P(M)=3920/5600=0.70 <BR>\n" );
document.write( "	c.	What is the probability that a randomly selected resident is a man and is in favor of building the bridge?<BR>\n" );
document.write( "Prob(M&F)= 0.25 as we figured above<BR>\n" );
document.write( "	d.	What is the probability that a randomly selected resident is a man?<BR>\n" );
document.write( "P(M)=3920/5600=0.70<BR>\n" );
document.write( "	e.	What is the probability that a randomly selected resident is in favor of building the bridge?<BR>\n" );
document.write( "P(F)=1680/5600=0.30<BR>\n" );
document.write( "	f.	What is the probability that a randomly selected resident is a man or in favor of building the bridge?<BR>\n" );
document.write( "P(M or F)= P(M)+P(F)-P(M&f)= [3920+1680-1400]/5600=4200/5600=0.75<BR>\n" );
document.write( "	g.	A randomly selected resident turns out to be male.  Compute the probability that he is in favor of building the bridge.<BR>\n" );
document.write( "P(F|M)= 1400/2240=0.625\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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