For example, you know that \(p(X \cap Y)\) is bounded above by \(p(X)\) and by \(p(Y)\) and thus by \(\min\{p(X),p(Y)\}\). If \(p(X) \gt 0.5\) and \(p(Y) \gt 0.5\) then \(X\) and \(Y\) must overlap. So \(p(X\cap Y)\) is bounded below by \(p(X)+p(Y)-1\). But, by definition, \(p(X \cap Y)\) is also bounded below by \(0\). So we have the following result: if you know \(p(X)\) and you know \(p(Y)\), then, you know