document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185121>Question 1185121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the probability of an IRS audit is 5.2 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.<BR>\n" );
document.write( "  What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)<BR>\n" );
document.write( " What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815879 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=815879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "odds for = probability for / probability against.<BR>\n" );
document.write( "odds against = probability against / probability for.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "example;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if probability of an event is .25, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "odds for = .25 / .75 = 1/3.<BR>\n" );
document.write( "odds against = .75 / .25 = 3/1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability of winning is .25 / (.25 + .75) = .25 / 1 = 1/4.<BR>\n" );
document.write( "probability of losing is .75 / (.25 + .75) = .75 / 1 = 3/4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the probability of an event occurring is .052, then:<BR>\n" );
document.write( "the probability of that event not occurring is 1 - .052 = .948.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the odds of that event occurring is .052 / .948.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the odds against that event occurring is .948 / .052.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in whole numbers, these ratios becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "odds for = 52 / 948<BR>\n" );
document.write( "odds against = 948 / 52\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "these ratios can be simplified to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "odds for = 13 / 237<BR>\n" );
document.write( "odds against = 237 / 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability for = 13 / (237 + 13) = 13 / 250 = .052<BR>\n" );
document.write( "probability against = 237 / (13 + 237) = 237 / 250 = .948\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you take .052 / .948 and multiply both sides by 1000 aqnd you get 52 / 948.<BR>\n" );
document.write( "that's where the whole numbers come from.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a reference on odds versus probabilities.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.thoughtco.com/how-are-odds-related-to-probability-3126553\" target = \"_blank\">https://www.thoughtco.com/how-are-odds-related-to-probability-3126553</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );