Question

In a game, three fair number cubes with faces numbered 1 through 6 are rolled. If the sum of the cubes is 16 or greater, a player wins 432 tokens; otherwise, the player wins nothing. Based on the given information, which number is equivalent to the fair number of tokens to pay for playing this game? A.8 B.12 C.14D.20

Answer 1

Solution

For this case the total outcomes are 6*6*6 = 216

The expected value is given by:

E(x) = p* X1 + (1-p)*X2

Where p = probability of success (sum of cubes 16 or greater)

and 1-p = probability of failure

X1 =