Chapter 8.5, Problem 55E

(a)

To determine

To find: The expected value of the player’s score when the player rolls one die.

(b)

To determine

To find: The expected value of the player’s score when the player rolls two dice.

(c)

To determine

To verify: That the expected non-zero score of a single die is 4, so that if a player rolls n dice that do not result in a score of 0, the expected score is 4n.

(d)

To determine

To verify: That there are $5^n$ possible ways to get a non-zero score and $6^n$ ways to roll the dice if the player rolls n dice and to explain why the expected value, $E=\frac{5^n\left(4n\right)}{6^n}$.