Two events E and F are independent. If $P(E) = 0.3$ and $P(E \cup F) = 0.5$, then $P(E/F) - P(F/E)$ equals to

Here, $P(E) = 0.3$ and $P(E \cup F) = 0.5$
Let $P(F) = x$

$= P(E) + P(F) - P(E) \cdot P(F)$
$\Rightarrow$ $0.5 = 0.3 + x - 0.3x$

$\Rightarrow$ $x = \frac{{0.5 - 0.3}}{{0.7}} = \frac{2}{7} = P(F)$

$\therefore$ $P(E/F) - P(F/E) = \frac{{P(E \cap F)}}{{P(F)}} - \frac{{P(F \cap E)}}{{P(E)}}$

$= \frac{{P(E \cap F) \cdot P(E) - P(F \cap E) \cdot P(F)}}{{P(E) \cdot P(F)}}$

$= \frac{{P(E \cap F)[P(E) - P(F)]}}{{P(E \cap F)}} = P(E) - P(F)$

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