Homework
For this Critical Thinking homework, you will apply concepts from probability theory to real-world scenarios.
Chicago is a group dice game that requires no skill. The objective of the game is to accumulate points by rolling certain combinations (GamezBuff, 2017).
How do you play Chicago?
i. There are eleven rounds in the game, one for each combination that can be made by adding two dice, namely the numbers two through 12. Each round has a target combination starting with two and going up all the way to 12.
ii. Going clockwise, the players take turns to roll both dice one time.
iii. If players roll the target combination, then they score points equal to the target combination, otherwise they score zero. For example, if the round corresponds to target combination six, then the player scores six points if the two dice add up to six. Else, the player scores no points.
iv. The player with the highest score at the end of the eleventh round wins the game.
Part I: Complete the following steps assuming the target combination is five:
i. What is the probability that the player rolls the target combination?
ii. What is the probability that the player rolls the target combination given that he/she rolled a one?
iii. What is the probability that the player does not roll the target combination given that he/she rolled a one?
iv. If the player wins a dollar for every point, he/she gets and losses three dollars for getting no points, what are the expected winnings or losses on each turn?
Part II: Based on your work in Part I, discuss the following:
i. Describe the sample space when rolling two dice once. How can identifying all the elements of the sample space help you answer the questions in Part I?
ii. Describe the relationship between odds and probability. Explain how you can use the result in question one, Part I to find the odds of getting the target combination in each turn.
iii. Determine if "rolling the target combination" and "rolling a one" are independent events. Justify your answer. Explain how this information can help you answer question two, Part I.
iv. Determine if "rolling the target combination given that the player rolled a one" and "not rolling the target combination given that the player rolled a one" are complementary events. Explain how you could have used the answer to question two, Part I to get the answer to question three, Part I.
v. Interpret the answer to question four, Part I.
vi. Discuss the advantages of understanding probabilities when playing dice games.
vii. Think of another scenario where probabilities can be used. Discuss the advantages of using probabilities in the context of the scenario you created.
Format your homework according to the following formatting requirements:
i) The answer should be typed, using Times New Roman font (size 12), double spaced, with one-inch margins on all sides.
ii) The response also includes a cover page containing the title of the homework, the student's name, the course title, and the date. The cover page is not included in the required page length.
iii) Also include a reference page. The Citations and references must follow APA format. The reference page is not included in the required page length.