Two dice are thrown independently. Let be the event that the number appeared on the die is less than the number appeared on the die, be the event that the number appeared on the die is even and that on the second die is odd, and be the event that the number appeared on the die is odd and that on the is even. Then:

The number of favourable cases of the event is . Explanation: Solution Total outcomes for two dice . Event ( ): Favourable cases are . Number of cases . Event ( even, odd): , . Number of cases . Event ( odd, even): , . Number of cases . Checking the options: Option 1: Incorrect ( and have 9 cases, not 6). Option 4: For and to be mutually exclusive, . Check for intersection: are in both and . So they are not mutually exclusive. Option 2: Evaluate . Since and are disjoint, this is . cases: . Total . Correct Option: (2)

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

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

Choose the correct answer: