Question

Two dice are thrown and the sum of the numbers which come up is noted. Among the following events: A: sum is even, B: sum is multiple of 3, C: sum is less than 4, D: sum is greater than 11. Which pair of events are mutually exclusive?

• A. A and B
• B. A and C
• C. C and D
• D. B and D

Hint:

Two events are mutually exclusive when no outcome is common between them. If even one outcome matches, they are not mutually exclusive.

Answer 1

The Correct Option is C

Concept: Two events are called mutually exclusive if they cannot occur at the same time. In probability terms, their intersection is an empty set: \[ A \cap B = \emptyset \] When two dice are thrown, the possible sums range from 2 to 12.

Step 1: Define each event clearly
We list all possible sums for each event: Event A (even sum): \[ \{2,4,6,8,10,12\} \] Event B (multiple of 3): \[ \{3,6,9,12\} \] Event C (sum less than 4): \[ \{2,3\} \] Event D (sum greater than 11): \[ \{12\} \]

Step 2: Check intersections
We check each option: (A and B): \[ \{2,4,6,8,10,12\} \cap \{3,6,9,12\} = \{6,12\} \neq \emptyset \] (B and D): \[ \{3,6,9,12\} \cap \{12\} = \{12\} \neq \emptyset \] (A and C): \[ \{2,4,6,8,10,12\} \cap \{2,3\} = \{2\} \neq \emptyset \] (C and D): \[ \{2,3\} \cap \{12\} = \emptyset \] Thus, only C and D are mutually exclusive.