Probability

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 :