(1) Since there are 10 teachers in science and 5 teachers in liberal arts, the sampling ratio is 2: 1, so science chooses 2 teachers and liberal arts chooses 1 teacher ... (2 points)

(2) Remember A as an event: there are exactly 1 female teachers among the teachers selected by the science group, so p (a) = c14c16c210 = 815 … (6 points).

(3) The possible values of ξ are 0, 1, 2,3, p (ξ = 0) = c24c13c210c15 = 225. p(ξ= 1)= C 24 C 12 C 2 10 C 15+C 16 C 14 C 13 C 2 10 C 15 = 28 75，

P(ξ= 3)= c26c 12c 2 10c 15 = 2 15，P(ξ= 2)= 1-2 25-8 75-2 15。

ξ0 1 23 P225 28 75 3 1 75 2 15...( 1 1)

∴ E(ξ)=…= 8 5 …( 13 points)