Two dice are thrown independently. Let $\mathrm{A}$ 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, $\mathrm{B}$ be the event that the number appeared on the $1^{\text {st }}$ die is even and that on the second die is odd, and $\mathrm{C}$ 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 :