document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177759>Question 1177759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the probability of an IRS audit is 5.3 percent for US taxpayers who file form 1040 and who earned 100,000.00 or more\r<BR>\n" );
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document.write( "What are the odds that such a taxpayer would be audited \r<BR>\n" );
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document.write( "What are the odds against such a taxpayer being audited\r<BR>\n" );
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document.write( "How do you figure this one out  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806861 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=806861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> odds and probability are related in the following way.\r<BR>\n" );
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document.write( "probability of an event occurring is the number of ways it can happen divided by the total number of ways it can either happen or not happen.\r<BR>\n" );
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document.write( "as an example:\r<BR>\n" );
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document.write( "a dice had 6 sides with each of the number 1 through 6 printed on each side.\r<BR>\n" );
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document.write( "when you roll the dice, one of the numbers is shown on the top side of the dice.\r<BR>\n" );
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document.write( "the probability of landing a 1 on top is 1 out of 6 because you have 6 possible numbers to be on the top side of the dice, but only one of them will be a 1.\r<BR>\n" );
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document.write( "so the probability of landing a 1 is 1 / 6.\r<BR>\n" );
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document.write( "that's the probability of success (landing a 1) divided by the probability of landing any number from 1 to 6.\r<BR>\n" );
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document.write( "the odds for an event to occur is the probability of the event occurring divided by the probability of the event not occurring.\r<BR>\n" );
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document.write( "the probability of landing a 1 is 1/6.<BR>\n" );
document.write( "the probability of not landing a 1 is 5/6.<BR>\n" );
document.write( "the odds of landing a 1 are 1/5.\r<BR>\n" );
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document.write( "likewise, the odds for an event not occurring is the probability of the event not occurring divided by the probability of the event occurring.\r<BR>\n" );
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document.write( "the probability of not landing a 1 is 5/6.<BR>\n" );
document.write( "the probability of landing a 1 is 1/6.<BR>\n" );
document.write( "the odds of not landing a 1 are 5/1.\r<BR>\n" );
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document.write( "note that (1/6) / (5/6) = (1/6) * (6/5) = (1 * 6) / (6 * 5 = 1/5.\r<BR>\n" );
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document.write( "note also that (5/6) / (1/6) = (5/6) * (6/1) = 5/1.\r<BR>\n" );
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document.write( "applied to your problem, you have:\r<BR>\n" );
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document.write( "probability of being audited is .053<BR>\n" );
document.write( "probability of not being audited is (1 - .053) = .947.\r<BR>\n" );
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document.write( "odds of being audited is .053 / .947 = .0559662091 to 1.\r<BR>\n" );
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document.write( "odds of not being audited is .947 / .053 = 17.86792453 to 1.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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