document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169619>Question 1169619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Among the candidates who apply for the post of Senior Accountant, 60% have<BR>\n" );
document.write( "more than 10 years of experience and 45% have the qualification of MBA. Of<BR>\n" );
document.write( "those candidates who have more than 10 years of experience, 35% do not have<BR>\n" );
document.write( "the qualification of MBA.\r<BR>\n" );
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document.write( "Given that a candidate does not have the qualification of MBA, what is the<BR>\n" );
document.write( "probability that the candidate has more than 10 years of experience?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851310 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=851310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem using conditional probability and Bayes' Theorem.\r<BR>\n" );
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document.write( "**Understanding the Problem**\r<BR>\n" );
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document.write( "We need to find the probability that a candidate has more than 10 years of experience, given that they don't have an MBA.\r<BR>\n" );
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document.write( "**Given Information**\r<BR>\n" );
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document.write( "* P(Exp > 10) = 0.60 (60% have more than 10 years of experience)<BR>\n" );
document.write( "* P(MBA) = 0.45 (45% have an MBA)<BR>\n" );
document.write( "* P(¬MBA) = 1 - P(MBA) = 1 - 0.45 = 0.55 (55% do not have an MBA)<BR>\n" );
document.write( "* P(¬MBA | Exp > 10) = 0.35 (35% of those with >10 years experience do not have an MBA)\r<BR>\n" );
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document.write( "**Solution**\r<BR>\n" );
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document.write( "1.  **Find P(Exp > 10 and ¬MBA):**\r<BR>\n" );
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document.write( "    * We know P(¬MBA | Exp > 10) = 0.35.<BR>\n" );
document.write( "    * Using the conditional probability formula: P(¬MBA | Exp > 10) = P(Exp > 10 and ¬MBA) / P(Exp > 10)<BR>\n" );
document.write( "    * P(Exp > 10 and ¬MBA) = P(¬MBA | Exp > 10) * P(Exp > 10) = 0.35 * 0.60 = 0.21\r<BR>\n" );
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document.write( "2.  **Apply Bayes' Theorem:**\r<BR>\n" );
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document.write( "    * We want to find P(Exp > 10 | ¬MBA), the probability that a candidate has more than 10 years of experience given they don't have an MBA.<BR>\n" );
document.write( "    * Bayes' Theorem: P(Exp > 10 | ¬MBA) = P(Exp > 10 and ¬MBA) / P(¬MBA)<BR>\n" );
document.write( "    * P(Exp > 10 | ¬MBA) = 0.21 / 0.55<BR>\n" );
document.write( "    * P(Exp > 10 | ¬MBA) ≈ 0.3818\r<BR>\n" );
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document.write( "**Final Answer**\r<BR>\n" );
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document.write( "The probability that a candidate has more than 10 years of experience, given that they do not have the qualification of MBA, is approximately 0.3818.<BR>\n" );
document.write( " </SPAN>\n" );
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