document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192535>Question 1192535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Higher education at two-year and four-year institutions. The following table gives the counts of U.S. institutions of higher education classified as public or private and as two-year or four-year:\r<BR>\n" );
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document.write( "           Public   Private\r<BR>\n" );
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document.write( "Two-year    1000    721\r<BR>\n" );
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document.write( "Four-year   2774    672\r<BR>\n" );
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document.write( "Convert the counts to probabilities and summarize the relationship between these two variables using conditional probabilities. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848973 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848973\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate the Total Number of Institutions**\r<BR>\n" );
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document.write( "* Total institutions = 1000 (Public, Two-year) + 721 (Private, Two-year) + 2774 (Public, Four-year) + 672 (Private, Four-year) <BR>\n" );
document.write( "* Total institutions = 5167\r<BR>\n" );
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document.write( "**2. Calculate Probabilities**\r<BR>\n" );
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document.write( "* **P(Public)** = (Public Two-year + Public Four-year) / Total = (1000 + 2774) / 5167 = 0.721 <BR>\n" );
document.write( "* **P(Private)** = (Private Two-year + Private Four-year) / Total = (721 + 672) / 5167 = 0.279<BR>\n" );
document.write( "* **P(Two-year)** = (Public Two-year + Private Two-year) / Total = (1000 + 721) / 5167 = 0.331<BR>\n" );
document.write( "* **P(Four-year)** = (Public Four-year + Private Four-year) / Total = (2774 + 672) / 5167 = 0.669<BR>\n" );
document.write( "* **P(Public and Two-year)** = 1000 / 5167 = 0.193<BR>\n" );
document.write( "* **P(Public and Four-year)** = 2774 / 5167 = 0.538<BR>\n" );
document.write( "* **P(Private and Two-year)** = 721 / 5167 = 0.139<BR>\n" );
document.write( "* **P(Private and Four-year)** = 672 / 5167 = 0.130\r<BR>\n" );
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document.write( "**3. Calculate Conditional Probabilities**\r<BR>\n" );
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document.write( "* **P(Two-year | Public)** = P(Public and Two-year) / P(Public) = 0.193 / 0.721 = 0.268<BR>\n" );
document.write( "* **P(Four-year | Public)** = P(Public and Four-year) / P(Public) = 0.538 / 0.721 = 0.747<BR>\n" );
document.write( "* **P(Two-year | Private)** = P(Private and Two-year) / P(Private) = 0.139 / 0.279 = 0.498<BR>\n" );
document.write( "* **P(Four-year | Private)** = P(Private and Four-year) / P(Private) = 0.130 / 0.279 = 0.466\r<BR>\n" );
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document.write( "**Summary of the Relationship**\r<BR>\n" );
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document.write( "* **Public institutions are more likely to be four-year institutions** (74.7%) than two-year institutions (26.8%).<BR>\n" );
document.write( "* **Private institutions are more likely to be two-year institutions** (49.8%) than four-year institutions (46.6%). \r<BR>\n" );
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document.write( "This analysis suggests a relationship between the type of institution (public vs. private) and the level of education (two-year vs. four-year).<BR>\n" );
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