JEE Main2012MathematicsSets and RelationsActual
Let X and Y are two events such that P(X Y=) P X (Y . ) Statement 1: P (X Y^ = P X^ (Y=0 ) . Statement 2: P(X) P Y 2) P X Y( )
Options
- AStatement 1 is false, Statement 2 is true.
- BStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
- CStatement 1 is true, Statement 2 is false.
- DStatement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
Correct answer
B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
Step-by-step solution
Let X and Y be two events such that P(X Y)=P(X Y) We know aligned & P(X Y)=P(X)+P(Y)-P(X Y) & P(X Y)=P(X)+P(Y)-P(X Y) & (from (1) & P(X)+P(Y)=2 P(X Y) aligned Hence, Statement -2 is true. Now, P (X Y^ )=P(X)-P(X Y) and P (X^ Y )=P(Y)-P(X Y) This implies statement-1 is also true.