The complement is all the other answers besides the one that is wanted , which is known as the event. Together, the event and complement cover all possible outcomes.
When trying to find the probability of something, all possible outcomes need to be determined. The outcomes are not what the problem solver wants to become the complement. For example, if May, June and July are the event, then January, February, March, April, August, September, October, November and December are the complement. They are not the months wanted but, when grouped with the months that are wanted, they represent all possible outcomes.