Question

Given two independent events A and B such that P (A) = 0.3 and P (B) = `0.6. Find P (A ∩ overlineB ) `.

Answer 1

Given: 
\[\text{ A and B are independent events.} \]
\[P\left( A \right) = 0 . 3\]
\[P\left( B \right) = 0 . 6\]

\[ P\left( A \cap \bar{B} \right) = P\left( A \right) P\left( \bar{B} \right)\]
\[ = P\left( A \right)\left[ 1 - P\left( B \right) \right]\]
\[ = 0 . 3 \times \left[ 1 - 0 . 6 \right]\]
\[ = 0 . 3 \times 0 . 4\]
\[ = 0 . 12\]