Q. If $A$ and $B$ are two independent events such that $P(B) = \frac{2}{7},P\left( A \cup B^{c} \right) = 0.8$, then$\ P(A)$is equal to
A) 0.1
B) 0.2
C) 0.3
D) 0.4
Explanation
(c)
Since, $P(B) = \frac{2}{7}$ and $P\left( A \cup B^{c} \right) = 0.8$
$P\left( B^{c} \right) = 1 - \frac{2}{7} = \frac{5}{7}$
Using, $P\left( A \cup B^{c} \right) = P(A) + P\left( B^{c} \right) - P(A).P(B^{c})$
$\Rightarrow 0.8 = P(A) + \frac{5}{7} - \frac{5}{7}P(A)$
$\Rightarrow 0.8 = \frac{5}{7} + \frac{2}{7}P(A)$
$\Rightarrow P(A) = 0.3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.