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

$\frac{1}{5}$

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