document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105926>Question 1105926</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Listed below is the population by state for the 15 states with the largest population. Also included is whether that state's border touches the Gulf of Mexico, the Atlantic Ocean, or the Pacific Ocean (coastline).<BR>\n" );
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document.write( "Rank	State	Population	Coastline<BR>\n" );
document.write( "1	California	38,802,500	Yes<BR>\n" );
document.write( "2	Texas	26,956,958	Yes<BR>\n" );
document.write( "3	Florida	19,893,297	Yes<BR>\n" );
document.write( "4	New York	19,746,227	Yes<BR>\n" );
document.write( "5	Illinois	12,880,580	No<BR>\n" );
document.write( "6	Pennsylvania	12,787,209	No<BR>\n" );
document.write( "7	Ohio	11,459,163	No<BR>\n" );
document.write( "8	Georgia	10,097,343	Yes<BR>\n" );
document.write( "9	North Carolina	9,943,964	Yes<BR>\n" );
document.write( "10	Michigan	9,909,877	No<BR>\n" );
document.write( "11	New Jersey	8,938,175	Yes<BR>\n" );
document.write( "12	Virginia	8,326,289	Yes<BR>\n" );
document.write( "13	Washington	7,061,530	Yes<BR>\n" );
document.write( "14	Massachusetts	6,745,408	Yes<BR>\n" );
document.write( "15	Arizona	6,731,484	No<BR>\n" );
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document.write( "Suppose three states are selected at random. Calculate the probability for the following:<BR>\n" );
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document.write( "a. None of the states selected have a population of more than 9   000   000. (Round your answer to 3 decimal places.)\r<BR>\n" );
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document.write( "b. Exactly one of the selected states has a population of more than 9   000   000. (Round your answer to 3 decimal places.)\r<BR>\n" );
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document.write( "c. At least one of the selected states has a population of more than 9   000   000. (Round your answer to 3 decimal places.)<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 #720815 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13208)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You are selecting 3 of the 15 states in the list, so the denominator of the probability fraction for all three cases is \"15 choose 3\": <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2815%2C3%29+=+%2815%2A14%2A13%29%2F%283%2A2%2A1%29+=+455 ALIGN=MIDDLE  ALT=\"C%2815%2C3%29+=+%2815%2A14%2A13%29%2F%283%2A2%2A1%29+=+455\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "In all three cases you are looking for states with populations of more than 9 million.  10 of the 15 have populations of more than 9 million; 5 do not.<br><BR>\n" );
document.write( "a) To have none of the three state you choose having populations over 9 million, you need to choose 3 of the 5 states with lower populations (5 choose 3) and none of the 10 with higher populations (10 choose 0).<br><BR>\n" );
document.write( "The probability for this case to 3 decimal places is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%285%2C3%29%2AC%2810%2C0%29%29%2FC%2815%2C3%29+=+%2810%2A1%29%2F455+=+.022 ALIGN=MIDDLE  ALT=\"%28C%285%2C3%29%2AC%2810%2C0%29%29%2FC%2815%2C3%29+=+%2810%2A1%29%2F455+=+.022\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "b) To have exactly one of the three state you choose having populations over 9 million, you need to choose 2 of the 5 states with lower populations (5 choose 2) and 1 of the 10 with higher populations (10 choose 1).<br><BR>\n" );
document.write( "The probability for this case to 3 decimal places is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%285%2C2%29%2A%28C%2810%2C1%29%29%29%2FC%2815%2C3%29+=+%2810%2A10%29%2F455+=+.220 ALIGN=MIDDLE  ALT=\"%28C%285%2C2%29%2A%28C%2810%2C1%29%29%29%2FC%2815%2C3%29+=+%2810%2A10%29%2F455+=+.220\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "c) This case is just the \"opposite\" or complement of the first case: \"at least one\" is the complement of \"none\".  So the probability for this case is 1-.022 = .978. </SPAN>\n" );
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