[填空题]
Sophie and Ella play a game. They each have five car0vot/m:f c/8dzh:qt pds showing roman numerals I,dzp 0o cv/m:tf8t/ qh:79ghtcg4z 4dk g;pc,q3cx g 4a V, X, L, C. Sophie lays her cards face up on the table in order I, V, X, L, C as shown in the follc;p4g 3qcc7gak d9h t 4gz,g4xowing 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 .
