Question

If P (A) = 0.3, P (B) = 0.6, P (B/A) = 0.5, find P (A ∪ B).

 

Answer 1

\[P\left( \frac{B}{A} \right) = \frac{P\left( A \cap B \right)}{P\left( A \right)}\]
\[ \Rightarrow 0 . 5 = \frac{P\left( A \cap B \right)}{0 . 3}\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 5 \times 0 . 3\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 15\]
\[\text{ Now },\]
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ = 0 . 3 + 0 . 6 - 0 . 15\]
\[ = 0 . 9 - 0 . 15\]
\[ = 0 . 75\]