Write a report that answers the following questions and meet the list of requirements that follows.

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.


  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?
  2. Three fair coins are flipped. Outcomes in the sample space are represented by strings such as HHT, HTH, and TTT.
    1. List all of the elements in the sample space.
    2. Express the event “there is at least one head, but no more than two heads” as a set. Show each of the possible combinations.
    3. What is the probability that there is at least one head rolled, but no more than two heads?
  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 12 face cards and four aces in a deck of cards.


  • Your paper should be 2-3 pages in length and should cite and integrate at least one credible outside source.
  • Include a title page, an introduction, a body, a conclusion, and a Reference list.
  • The introduction should summarize the problem and state what approach and method will be applied to solve it.
  • The body of your paper should answer the questions posed in the problem, explain how you approached and approached and answered the question or solved the problem, and for each question, show all steps involved.
  • The conclusion should summarize your findings and what you have determined from the data and your analysis, with a broader or personal perspective in mind when applicable.
  • As with all written assignments, provide in-text citations and a reference page.
  • Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.
  • Document formatting, citations, and style should conform to the APA Requirements. Refer to the document (attached at the bottom of the page) Calculating Tree Height as an example of how the paper is to be formatted.
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