(1) Let Ai mean that I (i(i=0 0, 1) among the three people have "healthy eyesight".

At most 1 person "vision health" is recorded as event a,

Then p (a) = p (A0)+p (a1) = c 315c320+c15c215c320 = 4957.

(2) The possible values of ξ are 0, 1, 2, 3,

P(ξ=0)=(34)3=2764，

p(ξ= 1)= c 13× 14×(34)2 = 2764，

P(ξ=2)=C23×( 14)2×34=964，

P(ξ=3)=( 14)3= 164，

The distribution list of ξ is:

? ξ? 0? 1? 2? 3? p？ 2764? 2764? 964? 164∴eξ=0×2764+ 1×2764+2×964+3× 164=34.