The complement of event \(A\) is the event “\(A\) does not happen.” It is the set of outcomes in the sample space \(S\) that are not in event \(A\). Note that the complement of an event in probability...The complement of event \(A\) is the event “\(A\) does not happen.” It is the set of outcomes in the sample space \(S\) that are not in event \(A\). Note that the complement of an event in probability is essentially the same as the complement of a set, since an event is a subset of the sample space. It is possible for a card to be both red and a 5 at the same time but it is not possible for a card to be both red and a spade at the same time.