Two dice are thrown independently. Let \(A\) be the event that the number on the \(1^{\text{st}}\) die is less than the number on the \(2^{\text{nd}}\) die; \(B\) be the event that the number on the \(1^{\text{st}}\) die is even and that on the \(2^{\text{nd}}\) die is odd; and \(C\) be the event that the number on the \(1^{\text{st}}\) die is odd and that on the \(2^{\text{nd}}\) die is even. Then: