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Question
If P (A ∪ B) = 0.8 and P (A ∩ B) = 0.3, then P \[\left( A \right)\] \[\left( A \right)\] + P \[\left( B \right)\] =
Options
0.3
0.5
0.7
0.9
Solution
0 . 9
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) = P\left( A \cup B \right) + P\left( A \cap B \right)\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) = 0 . 8 + 0 . 3\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) = 1 . 1\]
\[ \Rightarrow 1 - P\left( \bar{A} \right) + 1 - P\left( \bar{B} \right) = 1 . 1\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) = 2 - 1 . 1\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) = 0 . 9\]
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