University:
University of Houston
Course:
MATH 2312 | Precalculus
Academic year:

2022
Views:

215

Pages:

2
Author:

alarmesb63z

Game of Chuck-a-Luck In the game of Chuck-a-Luck three fair dice are rolled. You as the “bettor” are allowed to bet $1 on the occurrence of one of the integers 1, 2, 3, 4, 5, or 6. Suppose you bet on the occurrence of a “5”. Then if any 5’s occur on the 3 dice, you get your $1 bet back. In addition, if one 5 occurs (on the 3 dice) you win $1, if two 5’s occur you win $2, and if three 5’s occur you win $3. If no 5’s occur you lose your dollar. 1. In the long run, what amount of money would you expect to be paid (or lose) for one bet in the Chuck-a-Luck Game? 2. If you played 100 games, how much money would you expect to win (or lose)? Why? 3. Is the Chuck-a-Luck Game fair? Tree Diagram of Chuck-a-Luck Game 1/6 1/6 5 5/6 5 5 Not 5 5 P(X=3) = (1/6)3 (5/6)0 P(X=2) = (1/6)2 (5/6)1 P(X=2) = (1/6)2 (5/6)1 1/6 1/6 5/6 5/6 1/6 Not 5 5 5/6 Not 5 1/6 5 5/6 Not 5 5/6 Not 5 1/6 5/6 P(X=3) = 1/216 P(X=2) = 15/216 P(X=1) = (1/6)1 (5/6)2 P(X=2) = (1/6)2 (5/6)1 Not 5 1 2 P(X=1) = (1/6) (5/6) 5 1 2 P(X=1) = (1/6) (5/6) Not 5 0 3 P(X=0) = (1/6) (5/6) P(X=1) = 75/216 P(X=0) = 125/216 E(X) = -$1 (125/216) + $1 (75/216) + $2 (15/216) + $3 (1/126) = -$(17/216) ≈ -$0.08 On average, you should expect to lose approximately $0.08 each time you play a round of the game. In approximately 100 games, one should expect to lose $8. Although the first statement does not make much sense, it does provide us with information that allows us to make predictions about what will happen in the long run.