Question

If E and E₂ are independent evens, write the value of P \[\left( ( E_1 \cup E_2 ) \cap (E \cap E_2 ) \right)\]

 

Answer 1

\[P\left( \left( E_1 \cup E_2 \right) \cap \left( \bar{{E_1}} \cap \bar{{E_2}} \right) \right) = P\left( E_1 \cap \left( \bar{{E_1}} \cap \bar{{E_2}} \right) \right) \cup \left( E_2 \cap \left( \bar{{E_1}} \cap \bar{{E_2}} \right) \right)\]

\[= P\left( \phi \cup \phi \right) = 0\]