Chuck-a-luck (also sometimes called birdcage) is a game of chance played with th

Question

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 $1 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 are the number that you picked you win $10 (in each of these cases you also get your initial $1 bet back). If none of your number wind up being rolled you lose your $1 bet. Suppose that you play 5 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 both the amount and win or loss?

Explanation / Answer

a) Probability that triples of your number comes up is

3C3 * 1/6 * 1/6 * 1/6 = 1/216

Triples of he number occurs atleast - P(it doesn't occur at all)

=> 1 - 5C5 * (215/216)^5

=> 0.022934

B)

Probability of wininng 1 dollar = 1/2

Probability of winining 2 dollar = 1/12

Probability of winining 10 dollar = 1/216

Expected win or loss = 1/2 * 1 + 1/12 * 2 + 1/216 * 10 = 0.3015$

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