SOLUTION: 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?

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:  

minus 

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: 

 minus 

So there are 599 possible successes.

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

301:599

Edwin