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Question
If P (A) = \[\frac{6}{11},\] P (B) = \[\frac{5}{11}\] and P (A ∪ B) = \[\frac{7}{11},\] find
Solution
Given:
\[P\left( A \right) = \frac{6}{11}\]
\[P\left( B \right) = \frac{5}{11} \]
\[P\left( A \cup B \right) = \frac{7}{11}\]
\[\text { (i) P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ \Rightarrow \frac{7}{11} = \frac{6}{11} + \frac{5}{11} - P\left( A \cap B \right)\]
\[ \Rightarrow P\left( A \cap B \right) = \frac{6}{11} + \frac{5}{11} - \frac{7}{11} = \frac{4}{11}\]
\[\text{(ii) } P\left( A/B \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)}\]
\[ = \frac{\frac{4}{11}}{\frac{5}{11}}\]
\[ = \frac{4}{5}\]
\[\text {(iii) } P\left( B/A \right) = \frac{P\left( A \cap B \right)}{P\left( A \right)}\]
\[ = \frac{\frac{4}{11}}{\frac{6}{11}}\]
\[ = \frac{4}{6}\]
\[ = \frac{2}{3}\]
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