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For this Critical Thinking assignment, 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?

- 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.
- Going clockwise, the players take turns to roll both dice one time.
- 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.
- 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:**

- What is the probability that the player rolls the target combination?
- What is the probability that the player rolls the target combination given that he/she rolled a one?
- What is the probability that the player does not roll the target combination given that he/she rolled a one?
- 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:**

- 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?
- 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.
- 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.
- 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.
- Interpret the answer to question four, Part I.
- Discuss the advantages of understanding probabilities when playing dice games.
- Think of another scenario where probabilities can be used. Discuss the advantages of using probabilities in the context of the scenario you created.

**Requirements:**

You must submit two files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer.

The second file should be a 2-3-page narrative paper, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below:

- Your paper should be 2-3 pages in length (not counting the title page and references page) and should cite and integrate at least two credible outside sources. The CSU Global Library is a great place to find resources. Your textbook is a credible resource.
- Include a title page, introduction, body, conclusion, and a reference page.
- The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic.
- The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
- The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.

- Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables, graphs, etc.)
- Document formatting, citations, and style should conform to the . A short summary containing much that you need to know about paper formatting, citations, and references is contained in the . If you need assistance with your writing style or you need writing tips or tutorials, visit the .