Question

If $P \left( A _ { 1 } \cup A _ { 2 } \right) = 1 - P \left( A _ { 1 } ^ { c } \right) P \left( A _ { 2 } ^ { c } \right)$ where c stands for

Complement, then the events $A _ { 1 }$ and $A _ { 2 }$ are

• A. Mutually exclusive
• B. Independent
• C. Equally likely
• D. None of these

Answer 1

Answer: (B)

Independent

Answer 2

$P \left( A _ { 1 } \cup A _ { 2 } \right) = 1 - \left[ 1 - P \left( A _ { 1 } \right) \right] \left[ 1 - P \left( A _ { 2 } \right) \right]$

$= P \left( A _ { 1 } \right) + P \left( A _ { 2 } \right) - P \left( A _ { 1 } \right) \cdot P \left( A _ { 2 } \right)$.