Q. Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{\mathrm{st}}$ die is less than the number appeared on the $2^{\mathrm{nd}}$ die, $B$ be the event that the number appeared on the $1^{\mathrm{st}}$ die is even and that on the second die is odd, and $C$ be the event that the number appeared on the $1^{\mathrm{st}}$ die is odd and that on the $2^{\mathrm{nd}}$ is even. Then
A) The number of favourable cases of the event $(\mathrm{A}\cup\mathrm{B})\cap\mathrm{C}$ is 6
B) $A$ and $B$ are mutually exclusive
C) The number of favourable cases of the events $A$, $B$ and $C$ are $15, 6$ and $6$ respectively
D) $B$ and $C$ are independent
Explanation
The correct answer is Option A: The number of favourable cases of the event $(\mathrm{A}\cup\mathrm{B})\cap\mathrm{C}$ is 6.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.