document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203505>Question 1203505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jose is at a charity fundraiser and has a chance of receiving a gift. The odds in favor of receiving a gift are 4/19. Find the probability of Jose receiving a gift.\r<BR>\n" );
document.write( "\n" );
document.write( "A child has a box of candy which might have a toy inside. The probability of the box having a toy is 13/18. What are the odds against the box having a toy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839133 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Basic definitions....<br><BR>\n" );
document.write( "The \"odds in favor of\" compares number of good outcomes to number of bad outcomes.<br><BR>\n" );
document.write( "The \"odds against\" compares number of bad outcomes to number of good outcomes.<br><BR>\n" );
document.write( "The probability of an outcome compares the number of good outcomes to the number of all possible outcomes.<br><BR>\n" );
document.write( "Note: Probabilities are nearly always given as fractions (or decimals, or percentages).  Odds are usually given as ratios, e.g., A:B.   But sometimes, as in your post, they are also given as fractions, which I think is confusing.<br><BR>\n" );
document.write( "Examples...<br><BR>\n" );
document.write( "If the odds in favor of an outcome are 3:16, then the odds against are 16:3 and the probability is 3/(16+3) = 3/19.<br><BR>\n" );
document.write( "If the probability of an outcome is 3/8, then the odds in favor are 3:5 and the odds against are 5:3.<br><BR>\n" );
document.write( "If the odds against an outcome are 20:1, then the odds in favor are 1:20, and the probability is 1/21.<br><BR>\n" );
document.write( "Use those examples to answer your questions.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );