Given we know:
P(e) = .7,\; P(e | \neg s) = .15,\; P(\neg e|s) = .1<br />

Find P(s).
<br />
P(\neg e | s) = P(\neg e \cap s) / P(s) = .1

.1 P(s) = P(\neg e \cap s) = P(s \cap \neg e) = P(s) - P(s \cap e) <-- is this true?

=> .9 P(s) = P(s \cap e) -- (1)

P(e|\neg s) = P(e \cap \neg s)/P(\neg s) = .15

=> .15(1-P(s)) = P(e) - P(e \cap s)

since P(A \cap B) = P(A) - P(A \cap \neg B)\quad \forall A, B. <-- not sure about this identity, is it true?

=> .15 - .15 P(s) = .7 - .9 P(s) (by (1))

.75 P(s) = .55 \Rightarrow P(s) \approx .7333

is it correct?