(i) Set a pair of "it can be judged that two options are wrong" as event a,

"It can be judged that 1 option is wrong" is selected as event b,

"Unable to understand the meaning of the question" was selected as event C,

Then P(A)= 12, P(B)= 13, P(C)= 14,

∴ The probability of the candidate getting 40 points:

P=[P(A)]2？ P(B)？ p(C)= 14× 13× 14 = 148。

(2) ① Candidates' score ξ=20, 25, 30, 35, 40,

P(ξ=20)=[P(。 2P(。 B)P(。 C)= 14×23×34=648，

P(ξ=25)=C 12P(A)P(。 A)P(。 B)P(。 C)+[P(。 2P(B)P(。 C)+[P(。 2P(。 B)P(。 c)

=2×( 12)2×23×34+ 14× 13×34+ 14×23× 14= 1748,

P(ξ=30)=[P(A)]2P(。 B)P(。 C)+C 12P(。 A)P(A)P(。 B)P(C)+[P(。 2P(B)P(C)

=( 12)2×23×34+2× 12× 12×23× 14+2× 12× 12× 13×34+( 12)2× 13× 14= 1748,

P(ξ=35)=C 12P(A)P(。 P(B)P(C)+[P(A)]2P(。 B)P(。 c)

=2× 12× 12× 13× 14+( 12)2× 13×34+( 12)2×23× 14=748,

P(ξ=40)= 1-648？ 1748? 1748? 748= 148,

The candidate is most likely to get 25 or 30 points.

②eξ= 20×648+25× 1748+30× 1748+35×748+40× 148 = 335 12。