Given $P ( A )=0.3$ and $P ( B )=0.4$
(i) $P(A \cap B)$
When A and B are independent. Two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.
$\Rightarrow P(A\cap B)=P(A)\cdot P(B)$
$\Rightarrow P(A\cap B)=0.3\times 0.4\Rightarrow P(A\cap B)=0.12$
$(ii)$
As we know, $$P(A \cup B)=P(A)+P(B)-P(A \cap B)$$
$$\Rightarrow P(A \cup B)=0.3+0.4-0.12$$
$$\Rightarrow P(A \cup B)=0.58$$
(iii) $P ( A \mid B )$
As we know $$P(A \mid B)=\frac{P(A \cap B)}{P(B)}$$
$$P(A\mid B)=\frac{0.12}{0.4}\Rightarrow P(A\mid B)=0.3$$
$(iv)$
As we know $$P(B \mid A)=\frac{P(A \cap B)}{P(A)}$$
$$\Rightarrow P(B\mid A)=\frac{0.12}{0.3}\Rightarrow P(B\mid A)=0.4$$