Solution: (i) (i) Let "one game I white ball" be the event A i (i=, 0, 1, 2,3),

Then P(A 3 )=,

(ii) let "winning in a competition" be event B, then B=A 2 ∪A 3,

P(A 2 )=, A 2 and A 3 are mutually exclusive,

So p (b) = p (A2)+p (A3) =;

According to the meaning of the question, all possible values of x are 0, 1, 2.

P(X=0)=( 1﹣ ) 2 =，

p(x = 1)= c 2 1( 1﹣)=，

P(X=2)=( ) 2 =，

So the distribution list of x is

Mathematical expectation of x e (x) = 0.