JEE Main 2023 — Probability Question with Solution

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 :