Let X and Y are two events such that P ( X ∪ Y = ) PX ∩ ( Y . ) Statement 1: P ( X ∩ Y ′ = P ˙ X ′ ∩ ( Y = 0 ) Statement 2: P ( X ) P Y ∈ 2 ) PX ∩ Y ( )

Question

TestHub · Accepted Answer

Let X and Y be two events such that P ( X ∪ Y ) = P ( X ∩ Y ) We know ​ 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 ) ​ 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.

Mathematics - Sets and Relations Question with Solution | TestHub

Options:

Doubts & Discussion