document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119061>Question 1119061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. <BR>\n" );
document.write( "In the past, 25% of students who applied to University A were accepted, while University B accepted 35% of the applicants. <BR>\n" );
document.write( "Assume events are independent of each other. <BR>\n" );
document.write( "Give all the answers as DECIMAL NUMBERS! <BR>\n" );
document.write( "a.	What is the probability that you will be accepted in both universities? \r<BR>\n" );
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document.write( "b.	What is the probability that you will be accepted to at least one graduate program? \r<BR>\n" );
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document.write( "c.	What is the probability that one and only one of the universities will accept you? \r<BR>\n" );
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document.write( "d.	What is the probability that neither university will accept you?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734523 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52792)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. <BR>\n" );
document.write( "In the past, 25% of students who applied to University A were accepted, while University B accepted 35% of the applicants. <BR>\n" );
document.write( "Assume events are independent of each other. <BR>\n" );
document.write( "Give all the answers as DECIMAL NUMBERS! \r<BR>\n" );
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document.write( "a.  What is the probability that you will be accepted in both universities? \r\n" );
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document.write( "    P(A & B) = P(A)*P(B) = 0.25*0.35 = 0.0875.\r\n" );
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document.write( "b.  What is the probability that you will be accepted to at least one graduate program? \r\n" );
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document.write( "    P(A U B) = P(A) + P(B) - P(A)*P(B) = 0.25 + 0.35 - 0.0875 = 0.5125\r\n" );
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document.write( "c.  What is the probability that one and only one of the universities will accept you? \r\n" );
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document.write( "    P(A\B) + P(B\A) = P(A U B) - P(A & B) = 0.5125 - 0.0875 = 0.425.\r\n" );
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document.write( "d.  What is the probability that neither university will accept you? \r\n" );
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document.write( "    1 - P(A U B) = 1 - 0.5125 = 0.4875.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "All questions are answered.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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