Let X and Y are two events such that P(X | vedclass

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Question

Let $X$ and $Y$ be two events such that

$P(X \cup Y)=P(X \cap Y)$        .....$(1)$

We know

$P(X \cup Y)=P(X)+P(Y)-P(X \c

Vedclass · Accepted Answer

Statement $1$ is true, Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$ .

Vedclass · Answer

Let $X$ and $Y$ be two events such that

$P(X \cup Y)=P(X \cap Y)$        .....$(1)$

We know

$P(X \cup Y)=P(X)+P(Y)-P(X \cap Y)$

$P(X \cap Y)=P(X)+P(Y)-P(X \cap Y)$

(from $( 1)$)

$\Rightarrow P(X)+P(Y)=2 P(X \cap Y)$

Hence, Statement - $2$ is true

Now, $P\left(X \cap Y^{\prime}\right)=P(X)-P(X \cap Y)$

and $P\left(X^{\prime} \cap Y\right)=P(Y)-P(X \cap Y)$

This implies statement- $1$ is also true

Let $X$ and $Y$ are two events such that $P(X \cup Y=P)\,(X \cap Y).$

Statement $1:$ $P(X \cap Y' = P)\,(X' \cap Y = 0).$

Statement $2:$ $P(X) + P(Y = 2)\,P\,(X \cap Y)$

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