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Question
If P(A) = 0·4, P(B) = p, P(A ⋃ B) = 0·6 and A and B are given to be independent events, find the value of 'p'.
Solution
If A and B are independent events, then
\[P\left( A \cap B \right) = P\left( A \right)P\left( B \right)\]
\[ \therefore P\left( A \cap B \right) = 0 . 4p \left[ \because P\left( A \right) = 0 . 4 \text { and }P\left( B \right) = p \right]\]
As P(A ⋃ B) = 0·6
So,
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ \Rightarrow 0 . 6 = 0 . 4 + p - 0 . 4p\]
\[ \Rightarrow 0 . 2 = 0 . 6p\]
\[ \Rightarrow p = \frac{1}{3}\]
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