Question:
If A and B are any two events of a sample space, then set-theoretic description for the event "Exactly one of the events A, B to occur" is:
If A and B are any two events of a sample space, then set-theoretic description for the event "Exactly one of the events A, B to occur" is:
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To describe "exactly one" of two events using set theory, use the union of the event where one occurs and the other does not.
Updated On: May 15, 2025
- \( A \cap B^c \)
- \( (A - B) \cup (A \cup B) \)
- \( (A \cap B^c) \cup (A^c \cap B) \)
- \( (A \cap B^c)^c \cup (A^c \cap B^c) \)
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The Correct Option is C
Solution and Explanation
The event "Exactly one of A or B occurs" is described by the union of two disjoint events: either A occurs and B does not, or B occurs and A does not. This is given by \( (A \cap B^c) \cup (A^c \cap B) \).
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