# MATH 225N Discussion Probability

## Sample Answer for MATH 225N Discussion Probability Included After Question

**Initial Post Instructions**

Probability plays a major role in the medical community. Diagnoses are based on probabilities. They are really questions or “what if’s”, and are answered by the **probability** that the treatment will be the best for the ailment.

Let’s look at probability in terms of both the real world and the medical community.

- Survey 30 people to find out if they are left-handed or right-handed, and use the following chart to create a contingency table with the information.

## Left handed Right handed Total Female Male Total

- Answer the following questions about the information in your contingency table:
- If a person is randomly selected from the survey participants, what is the probability that the person will be left-handed?

- If you randomly choose a female from the people you surveyed, what is the probability that she is left-handed?

- What is the odds ratio of choosing a left-handed
**female**?

- What is the relative risk of choosing a left-handed
**female**?

## Example

Green | Blue | Total | |

Cats | 40 (A) | 20 (B) | 60 (A+B) |

Dogs | 30 (C) | 40 (D) | 70 (C+D) |

Total | 70 (A+C) | 60 (B+D) | 130 (A+B+C+D) |

- Probability of Green – (A+C)/(A+B+C+D): 70/130 = 0.54
- Probability of Green Cat – A/(A+B): 40/60 = 0.67
- Odds Ratio of Green Cat – (A/B)/(C/D) or AD/BC: (40
*40)/(20*30) = 1600/600 = 2.67 - Relative Risk of Green Cat – [A/(A+C)]/[B/(B+D)]: (40/70)/(20/60) = 1.71
- Skim through at least one of the following articles on left-handed vs. right-handed people from the Chamberlain Library. Answer the following question: How do the probabilities and percentages for your study compare to those in the study you read?

**Follow-Up Post Instructions**

## A Sample Answer For the Assignment: MATH 225N Discussion Probability

## Title: MATH 225N Discussion Probability

For grading purposes, this particular discussion posting area runs from Sunday Jan 24 through Sunday Jan 31, inclusively.

We explore ( mathematical ) Probability this Week. This includes probability concepts, conditional probability, independence, dependence, event( s ), the concept of “mutually exclusive,” the concept of “complement,” the multiplication rule, and the addition rule.

Please don’t forget to use an “**outside**” resource as part of the content and documentation for your first Post – the Post which is due on or before Wednesday of the Week – the Post where you make the most major contribution to the Weekly discussion posting area and attempt to address the discussion prompts / cues for the Week. It could possibly include a web site that you discovered on the internet at large, so long as the web site is relevant and substantial and does not violate the Chamberlain University policy for prohibited web sites, and so forth. It could possibly include references / resources that you discover through making use of the online Chamberlain University Library ( please click Resources along the left and then click Library to discover the link to the Chamberlain University online Library ) . 🙂

Check out the link below for some information about concepts such as independence, dependence, mutually exclusive, disjoint, complement, and conditional probability.

Link (Links to an external site.)Links to an external site.

This is one kind of an example of using an “outside” source / resource to add to what is revealed in our Weekly Lesson in Modules and in our Weekly text book reading.

Please don’t forget to look over the Graded Discussion Posting Rubric each Week to be certain that you are meeting all of the Frequency requirements as well as all of the Quality requirements for graded discussion posting each Week.

If you have any questions about anything, please do not hesitate to post in the Q & A Forum discussion posting area or to send me a direct e-mail message to [email protected]

Thanks Friends and Good Luck ! Work hard and learn a lot !!

Sincerely, Mr. Smith Chamberlain University Math, Statistics, and Quantitative Research

Please remember that **probabilities are NOT percentages** and so the answers ( no doubt approximate and rounded off ) in the examples about the green cat above should please be respectively.

**Click here to ORDER an A++ paper from our Verified MASTERS and DOCTORATE WRITERS MATH 225N Discussion Probability:**

**0.54 0.67** for the two probability questions and

the answer for the odds ratio question should be approximately **2.67** and

the answer for the relative risk question should be approximately **1.71**

You will want to please be very careful how you set up the rows and columns of your two way table ( which is also called a contingency table ) if you are hoping to make a perfect analogy between how the questions were worked out for the green cat and how the questions would be worked out for your left handed females.

Would the analogy work best if you set up your own two way table like this ??

Left Handed | Right Handed | Total | |

Females | |||

Males | |||

Total |

I am really asking ( this is not rhetorical ) because I am just glancing at this assignment for the first time this morning. 😉

Also your lower right cell here should be 30 .

And the sum of the four cells involving left handed females, right handed females, left handed males, and right handed males should be 30 as well.

That is, you survey 30 humans and each human is placed into one and only one of those 4 possible cells.

Then you compute and fill in column totals and row totals.

Then as you will see the Table Total or the Grand Total in the lower right will be 30 .

Once you set up your contingency table ( two way table ) correctly, answering the 4 questions will be a breeze. But give probabilities with answers like 0.XXXX please !!

**DON’T state a percentage as an answer to a probability question.**

Try hard to use one of the two provided links to find your “outside” reference / resource this Week 4 .

It would get boring though in a large class if EVERYONE did that. So please do that if you can but if a few Folks choose to find some other “outside” reference / resource this Week ( about left handedness and right handedness issues and trends and data ) that would certainly add some variety and freshness to our Week 4 graded Posting area.

Finally, many of you might make mistakes this Week, even though you have the example provided about the Green Cat( s )

So if you correct each other’s mistakes in follow up Posts, please be polite and sensitive and diplomatic and professional and all that – and I will try hard to do that as well. We are all Friends and fellow learners here.

Thanks Friends and here below are a couple Videos to watch if you are concerned that the one Green Cat( s ) example is not quite enough to make you feel confident and secure about all of this.

Thanks Friends and work hard this Week 4 ! Your commitment and energy and drive and motivation will be put to the test during this Week 4 !!!

his **Week 4** Recorded Office Hour Video ( **from a previous Academic Term** ) completely goes through the **Week 4 Knewton Homework assignment Contingency Tables** * TWICE* and provides a lot of great examples therefore that not only help you with the corresponding

**Week 4**Knewton Homework assignment but

*ALSO*the

**Week 4**graded Posting assignment. 😉

The first time through the assignment there were more **odds ratio** problems and exercises and the second time through the assignment there were more **relative risk** problems and exercises.

Both times through the assignment, there were a decent number of **conditional probability** problems and exercises.

Thanks Friends and this Video should really help you out both with the **Week 4 Contingency Tables Knewton homework assignment** as well as the **Week 4** Graded Discussion Posting assignment.

Good Luck and take good care and best wishes Friends !!

Thanks for your hard work, effort, and progress !!

🙂

We go through the homework assignments from beginning to end, showing you how to work on and complete them and showing you how to get them up to 100% full mastery and 10 / 10 points each in the CANVAS grade book. Thanks Friends and best wishes and take a look !!

In order to gather the following data, I asked fellow family members and friends what their dominant hand was. It resulted in the following table:

Female | Male | Total | |

Left-Handed | 4 | 5 | 9 |

Right-Handed | 15 | 6 | 21 |

Total | 19 | 11 | 30 |

- If a person is randomly selected from the survey participants, what is the probability that the person will be left-handed?
- 9/30 participants were left-handed.
- Probability: 9/30= 0.30

- If you randomly choose a female from the people you surveyed, what is the probability that she is left-handed?
- 19/30 participants were female. Of those who were female 4/19 were left-handed.
- Probability: 4/19= 0.21

- What is the odds ratio of choosing a left-handed female?
- (4/5)/(15/6)= 0.32

- What is the relative risk of choosing a left-handed female?
- [4/(4+15)]/[5/(5+6)] = (4/19)/(5/11)
- Relative Risk= 0.46

I skimmed through the first article linked in our discussion “Being a Lefty is All Right” according to Orr, 2001 10 to 13% of the world’s population is left-handed. I thought this was a fairly small percentage, but it is even smaller than in the sample I collected. This is not unexpectedly however, as the law of large numbers states “as our sample size increases the probability found in the sample size will be closer to the expected outcome” (Week 4 Lesson: Probability in Everyday Life, 2021). According to Mwaniki, 2018 10-12% of the world’s population is left-handed and of those who are left-handed, men are 23% more likely to be than women. The fact of men being more likely than women to be left-handed also held true in my sample study.

## References:

Mwaniki, A., (2018). What Percentage of The World Population Are Left Handed? *World Atlas. *https://www.worldatlas.com/articles/what-percentage-of-the-world-population-are-left-handed.htmlLinks to an external site.

Orr, T., (2001). Being a lefty is all right! *Current Health. 28*(2):12-13.

Week 4 Lesson: Probability in Everyday Life. (2021). Chamberlain University. https://chamberlain.instructure.com/courses/75447/pages/week-4-lesson-probability-in-everyday-life?module_item_id=10306877

## A Sample Answer 2 For the Assignment: MATH 225N Discussion Probability

## Title: MATH 225N Discussion Probability

Most class members will probably want to try to make a perfect analogy between the example about the blue / green cats / dogs and the assignment having to do with left handed / right handed males / females and I wonder if possibly the two way table ( the contingency table ) has to be set up the way that I have set it up in this Post here in order to do that ? 😉

I did double check the answers to your first two probability questions and I did agree with the answers that you got here. Great work !!

I purposely have not checked the answers to your odds ratio and relative risk questions yet. I am going to wait one more or two more days before doing that. I don’t want to give too much away before giving other class members a chance to work on the assignment and to struggle with the assignment.

Thanks Brennaa for your Terrific work and Fantastic results in the course !

I really appreciate it very much !

Please keep it up too ! Best Wishes Brennaa and Everyone !!!