A) Statement 1 is false. Statement 2 is true. Statement 1 is true. Statement 2 is true,
B) Statement 2 is not a correct explanation of Statement 1.
C) Statement 1 is true. Statement 2 is false.
D) Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
Correct Answer: B
Solution :
Let X and V be two events such that \[P\left( X\cup Y \right)=P\left( X\cap Y \right)\] ?(1) We know \[P\left( X\cup Y \right)=P\left( X \right)+P\left( Y \right)-P\left( X\cap Y \right)\] \[P\left( X\cap Y \right)=P\left( X \right)+P\left( Y \right)-P\left( X\cap Y \right)\] (from (1) \[\Rightarrow \]\[P\left( X \right)+P\left( Y \right)=2P\left( X\cap Y \right)\] Hence, Statement - 2 is true. Now, \[P\left( X\cap Y' \right)=P\left( X \right)-P\left( X\cap Y \right)\] and\[P\left( X'\cap Y \right)=P\left( Y \right)-P\left( X\cap Y \right)\] This implies statement-1 is also true.You need to login to perform this action.
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