In a game we will call “gambling dice,” you pay $1 to roll two dice. If you roll a sum of 5, 6, 7, or 8, you lose and don’t get your dollar back (you are out $1). If you roll anything else, you are given $2 (you have gained $1). 

a. When playing one game, what is the probability you will win? 

b. When playing one game, what is the probability you will lose? 

c. How much, on average, do you expect to win or lose per game, in the long run? In other words, what is the expected value of this game?