Question

Consider a game in which a player rolls 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 the roll is added to the total points. Any other roll is deducted from the player’s total. What is the expected value of the points earned on a single roll in this game?

Answer 1

$E_{roll}= \sum_{i=1}^{n} (x_i)(p_i)$
$E_{roll}= ((-1)(\frac{1}{6}))+((-2)(\frac{1}{6}))+((-3)(\frac{1}{6}))+((4)(\frac{1}{6}))+((5)(\frac{1}{6}))+((6)(\frac{1}{6}))$
$E_{roll}= (\frac{-1}{6})+(\frac{-1}{3})+(\frac{-1}{2})+(\frac{2}{3})+(\frac{5}{6})+(1)((6)(\frac{1}{6}))$
$E_{roll}= \frac{3}{2}$