document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194458>Question 1194458</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I calculate probability if I only have a percent and I unsure of the number of taxpayers who earned $100,000 or more?\r<BR>\n" );
document.write( "\n" );
document.write( "Suppose the probability of an IRS audit is 2.6 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.\r<BR>\n" );
document.write( "\n" );
document.write( "(a) What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)<BR>\n" );
document.write( "Odds that a taxpayer will be audited___to___\r<BR>\n" );
document.write( "\n" );
document.write( "(b) What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)<BR>\n" );
document.write( "Odds against a taxpayer being audited___to___<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826661 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=826661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the statement says:<BR>\n" );
document.write( "suppose the probability of an IRS audit is 2.6 percent for U.S. taxpayers who file form 1040 and who earned 100,000 or more.<BR>\n" );
document.write( "the statement is not asking you to determine the number of taxpayers who earned 100,000 or more.<BR>\n" );
document.write( "it is simply telling you that the probability is 2.6% that those people will be audited.<BR>\n" );
document.write( "no matter how small or large the group, past experience has indicated that approximately 2.6% of them will be audited.<BR>\n" );
document.write( "the determination of how small or large the group is doesn't matter. <BR>\n" );
document.write( "whatever the size of the group is, historical records indicate that 2.6% of them are audited.<BR>\n" );
document.write( "that means that the probability of any future group that possesses those characteristics (file a 1040 and earn more than 100,000 a year) is also 2.6%.<BR>\n" );
document.write( "that, i believe, is called empirical probability.<BR>\n" );
document.write( "it's probability based on historical evidence.<BR>\n" );
document.write( "the question is not concerned with that.<BR>\n" );
document.write( "it is concerned with determining odds that a taxpayer in that group will be audited or not audited.<BR>\n" );
document.write( "odds for equals probability that something will occur divided by probability that  something will not occur.<BR>\n" );
document.write( "odds against equals probability that something will not occur divided by probability that something will occur.<BR>\n" );
document.write( "in this problem, the probability that an audit will occur is 2.6%.<BR>\n" );
document.write( "the probability that an audit will not occur is therefore 100% minus 2.6% = 97.4%.<BR>\n" );
document.write( "the odds that the taxpayer in that group will be audited is therefore 2.6% / 97.4%, or 2.6 / 97.4 = .0266940454 = 13/487.<BR>\n" );
document.write( "the odds that the  taxpayer in that group will not be audited is therefore 97.4% / 2.6% = 97.4 / 2.6 = 37.46253846 = 487/13.<BR>\n" );
document.write( "i used the calculator to get these reduced fractions.<BR>\n" );
document.write( "without that, i would just say the odds for are 2.6/97.4 and the odds against are 97.4/2.6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "empirical probability is based on experience.<BR>\n" );
document.write( "if you flip a coin many times and the coin comes up heads 25% of the time and the coin comes up tails 75% of the time, then the probability becomes .25 to get heads and .75 to get tails.<BR>\n" );
document.write( "the odds of getting heads becomes .25 / .75.<BR>\n" );
document.write( "the odds of not getting heads becomes .75 / .25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability is defined as the number of ways an event can occur divided by the total number of ways.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "odds are defined as the number of ways an event can occur divided by the number of ways it cannot 0ccur.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your problem, experience has shown that taxpayers who file a 1040 and make more than 100,000, are audited 2.6% of the time.<BR>\n" );
document.write( "the probability they will get audited is therefore 2.6/100 = .026.<BR>\n" );
document.write( "the probability they won't get audited is therefore (1 - 2.6) / 100 = 97.4/100 = .974.<BR>\n" );
document.write( "the odds that they will get audited is 2.6/97.4, or .026/.974.<BR>\n" );
document.write( "the odda that they will not get audited is 97.4/2.6 = .974/.026.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "hope this helps.<BR>\n" );
document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );