Question

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

Answer 1

\[P\left( A \cup B \right) = P \left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[P\left( A \cup B \right) = P \left( A \right) + P\left( B \right) - P \left( A \right) \times P\left( B \right) \left[ \because \text{ A and B are independent events } \right]\]
\[ \Rightarrow 0 . 6 = 0 . 2 + P\left( B \right) - 0 . 2 \times P\left( B \right)\]
\[ \Rightarrow 0 . 6 - 0 . 2 = P\left( B \right)\left( 1 - 0 . 2 \right)\]
\[ \Rightarrow P\left( B \right) = \frac{0 . 6 - 0 . 2}{1 - 0 . 2}\]
\[ \Rightarrow P\left( B \right) = \frac{0 . 4}{0 . 8}\]
\[ \Rightarrow P\left( B \right) = \frac{1}{2}\]
\[ \Rightarrow P\left( B \right) = 0 . 5\]