If a and b are two independent events such that p(aub) =0.6 and p(a) = 0.2 then find p(b)

If A and B are two independent events such that P (A ∪ B) = 0.60 and P (A) = 0.2, find P(B).

\[P\left( A \cup B \right) = P \left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]\[P\left( A \cup B \right) = P \left( A \right) + P\left( B \right) - P \left( A \right) \times P\left( B \right) \left[ \because \text{ A and B are independent events } \right]\]\[ \Rightarrow 0 . 6 = 0 . 2 + P\left( B \right) - 0 . 2 \times P\left( B \right)\]\[ \Rightarrow 0 . 6 - 0 . 2 = P\left( B \right)\left( 1 - 0 . 2 \right)\]\[ \Rightarrow P\left( B \right) = \frac{0 . 6 - 0 . 2}{1 - 0 . 2}\]\[ \Rightarrow P\left( B \right) = \frac{0 . 4}{0 . 8}\]\[ \Rightarrow P\left( B \right) = \frac{1}{2}\]

\[ \Rightarrow P\left( B \right) = 0 . 5\]

Concept: Probability Examples and Solutions

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