If two independent events A and B are such that $P(A)=\frac{1}{2}$ and $P\left(\left(A' \cap B' \right)'\right) = \frac{3}{5}$, then P(B) is equal to
Answer & explanation
Correct answer: option 2
A, B → independent
$\Rightarrow P(A \cap B)=P(A) P(B)$
So $P(A)=\frac{1}{2}$
$P\left(\left(A' \cap B'\right)'\right)=\frac{3}{5}$
= $P(A \cup B) = \frac{3}{5}$ (Using de morgan's law)
so $P(A \cup B)=P(A)+P(B) - P(A \cap B)$
$\frac{3}{5}=\frac{1}{2}+P(B)-\frac{1}{2} P(B)$
⇒ 6 = 5 + 10((P(B)) - 5 P(B)
so $\frac{1}{5} = P(B)$
Option: B