document.write( "Question 447330: I am having trouble with probability. If the odds are 2:1 then the total chances is 3 and chances for is 2 and chances against is 1. is that correct? That makes the odds ratio .67/.33 or 2. (chances for / chances against).\r
\n" ); document.write( "\n" ); document.write( "if the probability is .18 then .82 is chances against or the odds are .22:1. Total chances is 100\r
\n" ); document.write( "\n" ); document.write( "is that correct? My biggest problem is determining odds against and odds in favor. Somehow I am getting this all mixed up.\r
\n" ); document.write( "\n" ); document.write( "Thanks\r
\n" ); document.write( "\n" ); document.write( "Randy \n" ); document.write( "
Algebra.Com's Answer #307963 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                     Number of successes\r\n" );
document.write( "Probability = —————————————————————-------------------\r\n" );
document.write( "               Number of success + Number of failures \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Odds in favor = Number of successes : Number of failures\r\n" );
document.write( "\r\n" );
document.write( "[Read the colon : as the word \"to\"]\r\n" );
document.write( "\r\n" );
document.write( "Odds against = Number of failures : Number of successes\r\n" );
document.write( "\r\n" );
document.write( "Ofentimes you will see Odds expressed so that it is \"something to one\"\r\n" );
document.write( "\r\n" );
document.write( "To express it \"to one\" form:\r\n" );
document.write( "\r\n" );
document.write( "                 Number of successes     \r\n" );
document.write( "Odds in favor = ————————————————————— : 1\r\n" );
document.write( "                 Number of failures \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                Number of failures     \r\n" );
document.write( "Odds against = ———————————————------ : 1\r\n" );
document.write( "                Number of successes \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the abreviations for the above formulas:\r\n" );
document.write( "      S\r\n" );
document.write( "P = —————\r\n" );
document.write( "     S+F \r\n" );
document.write( "\r\n" );
document.write( "Odds in favor = S:F\r\n" );
document.write( "\r\n" );
document.write( "Odds against = F:S\r\n" );
document.write( "\r\n" );
document.write( "if the probability is .18\r\n" );
document.write( "\r\n" );
document.write( "then .18 = 18/100 = 9/50 so S = 9 and S+F = 50\r\n" );
document.write( "\r\n" );
document.write( "So F = 50-S = 50-9 = 41\r\n" );
document.write( "\r\n" );
document.write( "So Odds in favor = S:F or 9:41\r\n" );
document.write( "\r\n" );
document.write( "Odds against = 41:9\r\n" );
document.write( "\r\n" );
document.write( "Or you can divide 41 and 9 by 9 and get\r\n" );
document.write( "\r\n" );
document.write( "Odds against = 4.6 to 1.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );