A game consists of drawing tickets with numbers on them from a box, independently with replacement. In order to play you have to stake $2 each time you draw a ticket. Your net gain is the number on the ticket you draw. Suppose there are 4 tickets in the box with numbers -2, -1, 0, 3 on them. If, for example the ticket shows $3 then you get your stake back, plus an additional $3.

a) Let X stand for your net gain in one game. What is the distribution of X? Find E(X) and Var(X).
b) If you play 100 times, what is your chance of winning $25 or more?