Question

A player rolls 2 dice. If the sum comes 2,3,4,5,6,8,9,10,11,12 the player wins 2$,3$,4$,5$,6$,6$,5$,4$,3$,2$ respectively but if the sum comes 7 the player loses 10$. Calculate the probabilities of winning at least three different amounts of money and the probability of losing the game. By using the probabilities, calculate the expected gain/loss per game and the theoretical standard deviation over a period of time.