Question:
A fair die is rolled once. Which one of the following is not true?
A fair die is rolled once. Which one of the following is not true?
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If two sets share even one element, they are NOT mutually exclusive.
Updated On: Apr 24, 2026
- $\{1,3\}$ and $\{2,4,6\}$ are mutually exclusive events
- $\{1,5\},\{2,4\}$ are $\{3,6\}$ mutually exclusive and exhaustive events
- $\{1,2,4,3,6,5\}$ is sure event
- $\{1\},\{2\}$ and $\{6\}$ are elementary events
- $\{1,3,2\}$ and $\{2,4,6\}$ are mutually exclusive events
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The Correct Option is
Solution and Explanation
Concept:
• Mutually exclusive events: no common elements
• Sure event: whole sample space
• Elementary event: single outcome
Step 1: Check Option (E)
\[ \{1,3,2\} \cap \{2,4,6\} = \{2\} \neq \emptyset \] So, not mutually exclusive.
Step 2: Check others briefly
(A) No common element $\Rightarrow$ true
(B) Covers full sample space $\Rightarrow$ true
(C) Contains all outcomes $\Rightarrow$ sure event
(D) Single outcomes $\Rightarrow$ elementary events Final Conclusion:
Option (E) is incorrect statement.
• Mutually exclusive events: no common elements
• Sure event: whole sample space
• Elementary event: single outcome
Step 1: Check Option (E)
\[ \{1,3,2\} \cap \{2,4,6\} = \{2\} \neq \emptyset \] So, not mutually exclusive.
Step 2: Check others briefly
(A) No common element $\Rightarrow$ true
(B) Covers full sample space $\Rightarrow$ true
(C) Contains all outcomes $\Rightarrow$ sure event
(D) Single outcomes $\Rightarrow$ elementary events Final Conclusion:
Option (E) is incorrect statement.
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