The two events $E$ and $F$ are independent. If $P(E)=0.3$ and $P(E \cup F)=0.5$, then $P(E / F)-P(F / E)$ is :

$\frac{1}{70}$

P(E) = 0.3,  P(E ∪ F) = 0.5

let P(F) = x

so P(E ∪ F) = P(E) + P(F) - P((E) - n(F))

⇒  P(E ∪ F) = P(E) + P(F) - P((F)

⇒ 0.5 = 0.3 + x - 0.3x

0.5 = 0.3 + 0.7x

so  0.2 = 0.7x ⇒  x = $\frac{2}{7}$ = P(F)

so  P(E/F) - P(F/E) = $\frac{P(E ∩ F)}{P(F)} - \frac{P(E ∩ F)}{P(E)} = \frac{P(E) P(F)}{P(F)} - \frac{P(E) P(F)}{P(E)}$

⇒  P(E) - P(F) = 0.3 - $\frac{2}{7}$

⇒ $\frac{3}{10}-\frac{2}{7}=\frac{21-20}{70}=\frac{1}{70}$