Question 608339
Suppose you select a 3-digit number at random from the set of all positive 3-digit numbers. What are the odds against a number greater than 400?
<pre>

Odds against = (number of possible failures):(number of possible successes)


The set of possible failures is the set of three-digit integers 
100 through 400, inclusive:  

{{{(matrix(8,1,

The,
400,
integers,
from,
1,
thru,
400,
inclusive))}}}minus{{{(matrix(8,1,The,
99,
integers,
from,
1,
thru,
99,
inclusive))}}} 

So the number of failures is 400 - 99 = 301

The set of possible successes is the set of three-digit integers 
401 through 999, inclusive: 

{{{(matrix(8,1,
The,
999,
integers,
from,
1,
thru,
999,
inclusive))}}} minus {{{(matrix(8,1,

The,
400,
integers,
from,
1,
thru,
400,
inclusive))}}}

So there are 599 possible successes.

Odds against = (number of possible failures):(number of possible successes) =

301:599

Edwin</pre>