Question

If $ A $ and $ B $ are two independent events such that $ P\left(B\right)=0.4 $ and $ P\left(A\cup B\right)=0.6 $ , then $ P\left(A\cap B\right)= $

• A. $ \frac{1}{3} $
• B. $ \frac{2}{3} $
• C. $ \frac{1}{5} $
• D. None of the above

Answer 1

Answer: (D)

We have,
$P(A\cup B) = P(A) + P(B) - P(A \cap B)$
$\Rightarrow 0.6 = P(A) + 0.4 - P(A) \cdot P(B)$
[$\because A$ and $B$ are independent events]
$\Rightarrow P(A) - 0.4 \times P(A) = 0.2 $
$\Rightarrow P(A) = \frac{0.2}{0.6} = \frac{1}{3}$
Now, $P(A\cap B) = P(A) \cdot P(B) $
$= \frac{1}{3} \times 0.4 = \frac{2}{15}$