[填空题]
Sophie and Ella play a game. w)p u:v imln;fga;.o;0rw,l wThey each have five cards-h xmh z17(uzc showing 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 fh-(17c zhz uxmollowing 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 .
