Question

$P(A\cup B)=P(A\cap B)$, if and only if the relation between $P\left(A\right)$ and $P\left(B\right)$ is $P\left(A\right)=P\left(B\right)$.If this is true enter 1,else enter 0

Answer 1

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
If $P(A\cup B)=P(A\cap B)$
Then $P\left(A\right)$ and $P\left(B\right)$ are equal
Since $P(A\cup B)=P(A\cap B)\Rightarrow A$ and $B$ are equal sets
Thus $P\left(A\right)$ and $P\left(B\right)$ are equal to $P(A\cap B)$