Question

$P ( A \cup B ) = P ( A \cap B )$if and only if the relation between $P ( A )$ and $P ( B )$ is

• A. $P ( A ) = P ( \bar { A } )$
• B. $P ( A \cap B ) = P \left( A ^ { \prime } \cap B ^ { \prime } \right)$
• C. $P ( A ) = P ( B )$
• D. None of these

Answer 1

Answer: (C)

$P ( A ) = P ( B )$

Answer 2

$P ( A ) = P ( B )$

As this gives $P ( A \cup B ) = P ( A ) + P ( B ) - P ( A \cap B )$

or $P ( A ) = 2 P ( A ) - P ( A )$ $\Rightarrow P ( A \cup B ) = P ( A \cap B )$