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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
(Here $\mathrm{E}^{\mathrm{c}}$ denotes the compliment of the event $\mathrm{E}$ )
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(Here $\mathrm{E}^{\mathrm{c}}$ denotes the compliment of the event $\mathrm{E}$ )
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Verified Answer
The correct answer is:
$\left(A \cap B^c\right) \cup\left(A^c \cap B\right)$
When only event $A$ occurs, then it can be written as $\left(A \cap B^C\right)$
And when only event B occurs, then it can be written as $\left(A^C \cap B\right)$
Then, 'exactly one of the events $A, B$ to occur' can be written as : $\left(A \cap B^C\right) \cup\left(A^C \cap B\right)$
And when only event B occurs, then it can be written as $\left(A^C \cap B\right)$
Then, 'exactly one of the events $A, B$ to occur' can be written as : $\left(A \cap B^C\right) \cup\left(A^C \cap B\right)$
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