If it has an emergency locator, what is the probability that it will be discovered? Okay so here's the question 

Seventy percent of the light aircraft that disappear while in flight
  in a certain country are subsequently discovered. Of the aircraft that
  are discovered, 60% have an emergency locator, whereas 90% of the
  aircraft not discovered do not have such a locator. Suppose that a
  light aircraft has disappeared. If it has an emergency locator, what
  is the probability that it will be discovered?

Anndd here's my answer

The answer to this question was, however, given as 93%. I don't understand how they got that answer and I was pretty confident in my solution. Can someone either tell me the answer given in the text is incorrect or what's wrong with my solution?
Thanks so much!

$P(D \mid E)$ 
$= P(D \cap E)/P(E)$
$= P(D \cap E)/P((E \cap D) \cup (E \cap \overline{D}))$
$= P(D \cap E)/\{P(E \cap D) + P(E \cap \overline{D})\}$
$= \{P(D) \cdot P(E \mid D)\}/\{(P(D) \cdot P(E \mid D)) + P(\overline{D}) \cdot P(E \mid \overline{D})\}$
$= (0.70 \cdot 0.60)/((0.70 \cdot 0.60) + (0.30 \cdot 0.10))$
$= 0.93$
