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