# Probability- Math Week 6 Critical Thinking (Essay Sample)

Option #1: Probability 1

Question #1

Find the odds in favor of a five being rolled on a single die. What is the probability of this event?

Question #2

Four poker players are all holding five cards. Two of the players are each holding three diamonds. What is the probability that the next card dealt will be a diamond?

Question #3

You are trying to analyze how much a customer is expected to spend at a local grocery store. Based on historical data, there are 50%, 30%, and 20% chances customers will spend $15, $20, and $25 respectively. What is the expected amount a customer will spend?

Requirements:

Show all your work so that the instructor clearly sees how you solved the problem.

Make sure your final answer is clear and visible.

Paper must be written in 3rd person.

Your paper should be about 4-5 pages in length or longer (counting the title page and references page) and cite and integrate at least one credible outside source. The CSU-Global Library(Links to an external site.)Links to an external site. (Links to an external site.) 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 importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.

The body of your paper should answer 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 the data and your analysis, often with a broader personal or societal perspective in mind. 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 associated with this problem in the body of your assignment.

Math Week 6 Critical Thinking

Name

MTH109-1 – Mathematical Explorations

Colorado State University – Global Campus

Instructor Date

Introduction

Probability is necessary to analyze random phenomena and for random experiments, there are a set of values that are determined by chance or the likelihood they may or may not occur. In probability, the sample spaces are used when there is a set possible outcome of a randomized experiment (CSU, 2016). An event is any subset of sample points and the theory of probability focuses on quantifying the chance of occurrence of an event chance and uncertainty. In situations where there are several possible outcomes, probability is necessary when there is focus on chance and uncertainty. When there is a large number of sample points, identifying the sample points and the associated probabilities is cumbersome and at times impossible (Anderson et al., 2017). Probability calculations are required for the analysis methods of the behavior of random phenomena such as rolling a die, choosing diamond from a deck of cards and the expected outcomes.

Rolling a dice

The odds in favor of a five being rolled on a single die and probability are determined. There are six sides of the dice and rolling a 5 is determined as probability of rolling a five divided by the probability of not rolling a fives. Thus p: q=1/6 ÷ 5/6= 1:5. The probability (p) of rolling a 5 is 1/ 6 or 16.7%, which is the number of fives÷ total possible outcomes while the probability (q) of not rolling a 5 is 5/6. In the case of throwing a dice, the more times the experiment is repeated, the more likely that the relative frequency, that is, the probability of occurrence of obtaining a 1, 2, 3, 4, 5 or 6 is 16.7%. Throwing of a dice is a random experiment, since the experiment can be repeated under the same conditions and all the possible outcomes are known despite not being sure of the final outcomes. All possible results of a randomized experiment as represented by the sample space is E = {1, 2, 3, 4, 5, 6}.

Classical probability represents the ratio between the number of favorable cases (events), and the total number of possible cases events where the events are mutually exclusive and equally possible. There is an assumption that events are equiprobable such that they have equal probability of occurring. An experiment in probability is any process or action that generates observations and that can be repeated including throwing a dice. Randomized experiments such as throwing a dice are based on chance, where they can be repeated indefinitely and always under the same conditions. Any subset of the sample is an event and the probability of occurrence of a given event, is the ratio between the number of times that event occurred a

### Other Topics:

- Discuss the pros and cons of the minimum wage. Does it benefit society or merely distort lab. . .Description: Undergraduate writing level 1 page Mathematics and Economics Format Style English (U.S.) Essay. Discuss the pros and cons of the minimum wage. Does it benefit society or merely distort labor markets? ...1 page/≈275 words | No Sources | APA | Mathematics & Economics | Essay |
- How firms benefit from economies of scale? (mod 4 SLP)Description: What might be some potential disadvantages of being part of a large corporation? Suppose business is booming at your firm. ...3 pages/≈825 words | 7 Sources | APA | Mathematics & Economics | Essay |
- Statistics Project: “Standard” Normal DistributionDescription: Compare Raw Data Distribution to Standard Normal Distribution. Using raw data gathered in Task 2 and the sample mean and sample standard deviation calculated ...2 pages/≈550 words | No Sources | APA | Mathematics & Economics | Essay |