Question

For any two independent events $E _ { 1 }$ and

$P \left\{ \left( E _ { 1 } \cup E _ { 2 } \right) \cap \left( \bar { E } _ { 1 } \cap \bar { E } _ { 2 } \right) \right\}$ is.

• A. $< \frac { 1 } { 4 }$
• B. $> \frac { 1 } { 4 }$
• C. $\geq \frac { 1 } { 2 }$
• D. None of these

Answer 1

Answer: (A)

$< \frac { 1 } { 4 }$

Answer 2

Since $\overline { E _ { 1 } } \cap \overline { E _ { 2 } } = \overline { E _ { 1 } \cup E _ { 2 } }$ and $\left( E _ { 1 } \cup E _ { 2 } \right) \cap \left( \overline { E _ { 1 } \cup E _ { 2 } } \right) = \phi$

$P \left\{ \left( E _ { 1 } \cup E _ { 2 } \right) \cap \left( \overline { E _ { 1 } } \cap \overline { E _ { 2 } } \right) \right\} = P ( \phi ) = 0 < \frac { 1 } { 4 }$.