[填空题]
Sophie and Ella play a game. They each have five cards shxpkq2(u c0 g5no/qo( fo84 /m1aow+.dh0j+ uwwopvsq.r mli a;wing roman numerals I, V, X, L, C. Sophie lays her cards face up on the table in order I, V, X, L, C as shown in the folloo h aq8r;ww l.d0i/mv1+su o4 .a+pjwmwing diagram.
Ella shuffles her cards and lays them face down on the table. She then turns them over one by one to see if her card matches with Sophie's 4 card directly above. Sophie wins if no matches occur; otherwise Ella wins.
1. Show that the probability that Sophie wins the game is $\frac{11}{30}$ .
Sophie and Ella repeat their game so that they play a total of 90 times. Let the discrete random variable X represent the number of times Sophie wins.
2. Determine:
1. the mean of X ;
2. the variance of X .
