Consider a game in which players roll a number cube to determine the number of points earned. if a player rolls a prime number, that many points will be added to the player’s total. any other roll will be deducted from the player’s total. what is the expected value of the points earned on a single roll in this game?

The expected value of the points earned on a single roll in the game would take into account the probability of the numbers of the cube and whether or not they're prime. If the cube is a dice with numbers 1 to 6, then the expected value of the points would be:
P = 1(1/6) + 2(1/6) + 3(1/6) - 4(1/6) + 5(1/6) - 6(1/6)
P = 1/6 or 0.1667