Question

Consider a game in which a player rules a number cube to determine the number of points earned. If a player rolls a number greater than or equal to 4 the number of roll is added to the total points. Any other roll is deducted from the players total. What is the expected value of the points earned on a single roll in this game?

Answer 1

Expected value is the sum of probabilities for all outcomes...

4*(1/6)+5*(1/6)+6*(1/6)-3*(1/6)-2*(1/6)-1*(1/6)

(4+5+6)/6-(3+2+1)/6

15/6-6/6

9/6

1.5

So the expected value for a single roll in this game is 1.5 points.