Q. The probability that at least one of the events $A$ and $B$ occurs is 0.6. If $A$ and $B$ occur simultaneously with probability 0.2, then $P\left( \overline{A} \right) + P(\overline{B})$ is
A) 0.4
B) 0.8
C) 1.2
D) 1.4
Explanation
(c)
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\therefore 0.6 = P(A) + P(B) - 0.2$
$\Rightarrow P(A) + P(B) = 0.8$
$\Rightarrow P\left( \overline{A} \right) + P\left( \overline{B} \right) = 12\ \ \lbrack\because P(A) = 1 - P\left( \overline{A} \right)\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.