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2 pages/≈550 words
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Mathematics & Economics
Other (Not Listed)
English (U.S.)
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Probability (Other (Not Listed) Sample)


Write a paper that adheres to the Written Assignment Requirements in the CSU-Global Guide to Writing and APA Requirements. In addition, the items noted in the Good Writing Tips section should be observed.
Your paper should contain a title page, an introduction, a body, a conclusion, and possibly a list of references. The introduction should provide background information about your paper topic, and it should state what your paper will address. We often state the main idea or purpose of the paper in what is termed a thesis statement.
The body of your paper details your methodology, findings, and/or the results of analysis. APA requires that tables, figures, and calculations/formulas used in your paper appear in the paper body.
The conclusion is where we summarize our findings, state other conclusions, relay personal experiences, and sometimes discuss the “take-home” messages associated with our work. As with many written assignments, in-text citations and a reference page are often included.
Be sure to describe or define probability, sample space, event, and possibly other terms in your paper introduction. Include calculations and solutions in the body of your paper.
In your paper, answer the following three questions:
Question #1 
The probability of being dealt two pairs in a five card poker hand is 0.0475. What are the odds of being dealt two pairs?
Question #2 
Three fair coins are flipped. Outcomes in the sample space are represented by strings such as HHT, HTH, and TTT.
List all of the elements in the sample space.
Express the event “there is at least one head, but no more than two heads” as a set. Show each of the possible combinations.
What is the probability that there is at least one head rolled, but no more than two heads?
Question #3 
Four cards are chosen from a 52-card deck. What is the probability that four cards are either face cards or aces? There are twelve face cards and four aces in a deck of cards.


Probabilities show the likelihood of an event occurring, whereby a probability of 0 indicates an event would not occur. On the other hand, a probability of 1 indicates that it is an event (s) will occur. Probability is dependent on the favorable outcomes and the total number of outcomes (Jaynes & Bretthorst, 2007). An event is most likely to occur when it is closer to 1. The probability of two independent events occurring is the product of their probabilities. Additionally, the probability of one event or another independent event occurring is the sum of their probabilities (Downing & Clark, 2010). A sample space represents the possible outcome and the probability that all the outcomes will occur is 1. An event is a subset in a sample space. Probability is to be calculated based on the favorable outcomes and total number of outcomes, in the three case scenarios.
[1] The probability of being dealt two pairs in a five card poker hand is 0.0475. What are the odds of being dealt two pairs?
The probability distribution of coin tossing gives the probability that an event will occur when tossed n times, and since the number of possibilities is finite, it is also known as the probability mass function (Hollos & Hollos, 2012). The four types ...
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