9 A game is played with a token on a board with a grid printed on it. The token starts at the point \(( 0,0 )\) and moves in steps. Each step is either 1 unit in the positive \(x\)-direction with probability 0.8 , or 1 unit in the positive \(y\)-direction with probability 0.2 . The token stops when it reaches a point with a \(y\)-coordinate of 1 . It is given that the token stops at \(( X , 1 )\).

1. (a) Find the probability that \(X = 10\).
   (b) Find the probability that \(X < 10\).
2. Find the expected number of steps taken by the token.
3. Hence, write down the value of \(\mathrm { E } ( X )\).