document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206559>Question 1206559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have.<BR>\n" );
document.write( "x	P(x)	xP(x)<BR>\n" );
document.write( "0	0.15	<BR>\n" );
document.write( "1	0.20	<BR>\n" );
document.write( "2	0.35	<BR>\n" );
document.write( "3		<BR>\n" );
document.write( "4	0.10	<BR>\n" );
document.write( "5	0.05	<BR>\n" );
document.write( "6 (or more)	0.05	<BR>\n" );
document.write( "(a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.)<BR>\n" );
document.write( "(c) Find the expected value. (Enter your answer to two decimal place.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844114 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=844114\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "X = number of children married people have<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >x</TD><TD >P(x)</TD></tr><tr><TD >0</TD><TD >0.15</TD></tr><tr><TD >1</TD><TD >0.20</TD></tr><tr><TD >2</TD><TD >0.35</TD></tr><tr><TD >3</TD><TD >????</TD></tr><tr><TD >4</TD><TD >0.10</TD></tr><tr><TD >5</TD><TD >0.05</TD></tr><tr><TD >6 (or more)</TD><TD >0.05</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "The two key rules for a probability distribution are:<ul><li>Each P(x) item must be between 0 and 1.</li><li>All of the P(x) values must add to 1.</li></ul>So,<BR>\n" );
document.write( "P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6) = 1<BR>\n" );
document.write( "0.15+0.20+0.35+P(3)+0.10+0.05+0.05 = 1<BR>\n" );
document.write( "0.9+P(3) = 1<BR>\n" );
document.write( "P(3) = 1 - 0.9<BR>\n" );
document.write( "P(3) = <font color=red>0.1</font>\r<BR>\n" );
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document.write( "The probability a married adult has exactly 3 kids is <font color=red size=4>0.1</font>\r<BR>\n" );
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document.write( "This is what the completed table will look like<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >x</TD><TD >P(x)</TD></tr><tr><TD >0</TD><TD >0.15</TD></tr><tr><TD >1</TD><TD >0.20</TD></tr><tr><TD >2</TD><TD >0.35</TD></tr><tr><TD >3</TD><TD ><font color=red>0.10</font></TD></tr><tr><TD >4</TD><TD >0.10</TD></tr><tr><TD >5</TD><TD >0.05</TD></tr><tr><TD >6 (or more)</TD><TD >0.05</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "--------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Now to fill out the column labeled x*P(x).<BR>\n" );
document.write( "As the name of this column suggests, we'll multiply each paired x and P(x) value.<BR>\n" );
document.write( "Eg: 0*0.15 = 0 and 1*0.20 = 0.20<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >x</TD><TD >P(x)</TD><TD >x*P(x)</TD></tr><tr><TD >0</TD><TD >0.15</TD><TD >0</TD></tr><tr><TD >1</TD><TD >0.20</TD><TD >0.20</TD></tr><tr><TD >2</TD><TD >0.35</TD><TD >0.70</TD></tr><tr><TD >3</TD><TD >0.10</TD><TD >0.30</TD></tr><tr><TD >4</TD><TD >0.10</TD><TD >0.40</TD></tr><tr><TD >5</TD><TD >0.05</TD><TD >0.25</TD></tr><tr><TD >6 (or more)</TD><TD >0.05</TD><TD >0.30</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "The \"6 (or more)\" entry at the bottom is treated simply as x = 6. I wasn't sure how to handle that portion. <BR>\n" );
document.write( "Spreadsheet software is recommended. But since the table is fairly small, doing it by hand isn't that bad. \r<BR>\n" );
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document.write( "Add up the values in the x*P(x) column to arrive at the <font color=red size=4>expected value 2.15</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );