Chuckaluck also sometimes called birdcage is a game of chanc

Chuck-a-luck (also sometimes called birdcage) is a game of chance played with three 6-sided dice. In the game you can pick any number from 1 to 6 and the three dice are then -rolled- in a cage. If $I is bet and exactly one of the number that you picked is rolled then you win $1. if exactly two of the number that you picked are rolled you win $2. and if all three of the dice arc the number that you picked you win $6 (in each of these cases you also get your initial $I bet back). If none of your number winds up being rolled you lose your SI bet. Suppose that you play 8 games of chuck-a-luck and pick the same number each time. a) What is the probability that triples of your number (all three dice come up your number) occurs at least once? b) What is your total expected win or loss? Indicate in your answer both the amount and win or loss.

Solution

a)

Probability that occurs at least once

1/6 + 1/6*1/6 + 1/6*1/6*1/6 = 0.1991

b)

expected win or loss

1*1/6 - 1 + 2* 1/6*1/6 - 1 + 6* 1/6*1/6*1/6 - 1 = -0.833 - 0.94 - 0.97 =-2.75

amount -2.75

loss