Question

You roll a fair die until a value other than 1 appears and are paid the amount on the die that appears on the last roll. What is the fair value of this game?

A. 1.17

B. 2.33

C. 3.50

D. 4.17

Answer 1

The fair value of the game is 3.50.

Step-by-step explanation:

To find the fair value of the game, we need to calculate the expected value. The expected value is the sum of the products of each outcome and its probability. In this game, the values on the die are {1, 2, 3, 4, 5, 6} and the probabilities are {1/6, 1/6, 1/6, 1/6, 1/6, 1/6}.

The expected value is calculated as follows:

Expected Value = (1/6 * 1) + (1/6 * 2) + (1/6 * 3) + (1/6 * 4) + (1/6 * 5) + (1/6 * 6)

Expected Value = 3.5

Therefore, the fair value of this game is 3.50 (option C).