The more conditions there are, the less likely an event becomes

For any possible set of events, the likelihood of A occurring will always be greater than the likelihood of A and B both occurring.If we took a random sample of a million people who majored in math,the subset who are portrait artists might be relatively small.But it will necessarily be bigger than the subset who are portrait artists and play poker.Anyone who belongs to the second group will also belong to the first?but not vice versa.The more conditions there are, the less likely an event becomes.