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Question
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find \[P \overline A \cup \overline B \] .
Solution
\[\text{ Given } : \]
\[\text{ A and B are independent events } .\]
\[P\left( A \right) = 0 . 3\]
\[P\left( B \right) = 0 . 6\]
\[P\left( \bar{A} \cap \bar{B} \right) = P\left( \bar{A} \right) P\left( \bar{B} \right)\]
\[ = \left[ 1 - P\left( A \right) \right]\left[ 1 - P\left( B \right) \right]\]
\[ = 0 . 7 \times 0 . 4\]
\[ = 0 . 28\]
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