# Unit 2 Discussion: Probability and Probability Distributions

The **Monty Hall problem** is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show *Let's Make a Deal* and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the *American Statistician* in 1975. It became famous as a question from a reader's letter, quoted in Marilyn vos Savant's "Ask Marilyn" column in *Parade* magazine in 1990:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

1. Would you stay with your original door selection, or would you switch? Explain your reasoning.

2. Watch at least one of the following videos about the Monty Hall Problem.

(If you would like additional explanation, you can watch the following additional videos:

Monty Hall Problem for Dummies or Probability and the Monty Hall Problem or The Monty Hall Problem - Explained )

**Indicate which video(s) you watched.** If you found another one on your own, include the link.

3. What is the probability of winning if you stay with your original door selection?

4. What is the probability of winning if you switch to the other door, after you've been shown the door with a goat?

5. Write a paragraph explaining why a contestant should switch doors on the game show.

Note: Parts of this discussion were based on CC LICENSED CONTENT, ORIGINAL

- Discussion: Probability.
**Provided by**: Lumen Learning.**License**:*CC BY-SA: Attribution-ShareAlike*

Video Citations:

- Numberphile (2014, May 22).
*Monty Hall Problem*[Video]. | Youtube | 5.30 min. - Numberphile (2014, May 28).
*Monty Hall Problem for Dummies*[Video]. | Youtube | 4.17 min. - Khan Academy (2012, Jun 27).
*Probability and the Monty Hall Problem*[Video]. | Youtube | 7.22 mins. - AsapSCIENCE (2012, Nov 6).
*The Monty Hall Problem - Explained*[Video]. | Youtube| 2.47 mins.

## Unit 2 Discussion: Probability and Probability Distributions

Unit 2 Discussion: Probability and Probability Distributions

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**1. Would you stay with your original door selection or switch? Explain your reasoning.**

I would switch. The reasoning used in constructing the switching is based on probability theory. At this point, the odds are still simple: the chance of choosing the car is 1/3, while the chance of the car being behind one of the other two doors is 2/3. If the host initiating the door-opening knows what is behind the doors and if he opens one of the remaining doors to show a goat, the probability distribution remains the same. Rather, the initial probability of 2/3 that the car is behind the other of the two doors is now 100% the one left unopened. Hence, to sum it up, switching more than doubles your chances of winning to 2/3.

**2. Indicate which video(s) you watched. If you found another one on your own, include the link.**

I watched the following videos:

- Numberphile (2014, May 22).
*Monty Hall Problem*[Video]. | Youtube | 5.30 min. - AsapSCIENCE (2012, Nov 6).
*The Monty Hall Problem - Explained*[Video]. | Youtube| 2.47 mins.

**3. What is the probability of winning if you stay with your original door selection?**

If you stay with your original door selection, the probability of winning is 1/3. Here's the calculation:

- When you pick one of the three doors initially, there is a 1/3 chance that the car is behind that door.
- It means there is a 2/3 chance that the car is behind one of the other two doors.

So, the probability of winning by staying with your initial choice is 1/3.

**4. What is the probability of winning if you switch to the other door after you've been shown the door with a goat?**

The probability of winning if you switch to the other door is 2/3. Here's the calculation:

- Initially, there is a 1/3 chance that the car is behind your chosen door and a 2/3 chance that it is behind one of the other two doors.
- Knowing what is behind each door, the host opens one of the remaining two doors to reveal a goat. This action doesn't change the initial probabilities.
- Since one of the other doors has been shown to have a goat, the entire 2/3 probability that the car is behind one of the two remaining doors now transfers to the one unopened door.

So, the probability of winning by switching is 2/3.

**5. Write a paragraph explaining why a contestant should switch doors on the game show.**

A contestant should switch doors in a game show because, given the data, the probability of their winning is higher when they switch. When the car is chosen initially, the probability is equal to 1/3, while after the host has opened one of the other two doors, the likelihood that the car is behind one of those doors is equal to 2/3. Because when the host opens a door with a goat behind it, the 2/3 probability of the car moving to be behind the other unopened door. In this way, the contestant is switching gains on a 2/3 likelihood of this case. As I said, the first choice offers a 1/3 chance of success if no switching is done, while switching doors raises the chances to 2/3, making this the best strategy in the event of repetitive plays. This odd outcome is supported by algebraic and simulation insights into probability, similar to other Strategic Decision-Making Games.

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Unit 2 Discussion: Probability and Probability Distributions

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**Pirated Software**

Pirated software is the use of software that allows others to copy, distribute, and operate other programs. Pirated software is an ethical issue due to digital theft and denying another individual who has rightfully designed a life out of software development (Cascavilla et al., 2021). The consequences of using pirated software are that other software developers have been led to legal risks owing to the respective demands of their users. This paper focuses on determining how pirated software is an ethical issue when marketing connected devices.

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Part I: Comprehension

Introduction

· Yes, the authors are qualified as all of them are scholars and teach at various universities, such as the University of West Georgia and the University of Nevada in the Department of Nursing and psychology, which are relevant to the study.

**Germany**

Germany is one of the largest countries in Europe by land mass; this has largely contributed to its popularity, making it one of the most known countries of the Nordic region. Besides being populous, the country enjoys the largest economy in Europe, which is mainly driven by three sectors: agriculture, service, and industry sectors. The country's large portion of the population is middle-income and is largely contributed by the service, industry, and agriculture sectors. Ever since its unification in the 20^{th} century, the country has seen numerous politically motivated events that have seen the country be plunged into the First and Second World Wars, with the latter leaving the country divided between two political ideologies. The focus of this paper is to determine how culture, legislation, economic and political systems have impacted the conduction of business in the country.

The manager should not be allowed to disclose the information of a tenant as the latter has a reasonable expectation of privacy unless the information is relevant in regard to the safety of other tenants (Porro, 2019). Thus, the manager should ensure that other tenants follow through with the directive and not have their indifferences determine their tenancy. In summation, the manager should withhold the information to prevent others from having access to it and should accord the new applicant as a potential tenant who has no bearing in regard to political indifferences that have caused a rift between the two parties.

Policy topic: __ GUN CONTROL __

Directions: Do some research and find 3 existing or proposed recent U.S. policies (laws, statutes, etc.) published or proposed on this topic. Do __not__ describe policies proposed/implemented prior to 2000. In addition to a brief description of the policy, you will also indicate the stance (for or against), level of implementation, and provide a link to the actual policy.

**Policy 1**

Policy name (Precise bill/policy/legislation name): __ Bipartisan Safer Communities Act (BSCA) gun safety bill. __

Policy link (Include a direct link to the policy. Do not use Wikipedia, news articles, etc. Go directly to the source for information): __ https://www.whitehouse.gov/briefing-room/statements-releases/2023/03/14/fact-sheet-president-biden-announces-new-actions-to-reduce-gun-violence-and-make-our-communities-safer/ __

A multicultural workplace has become a trend rather than an exception in many organizations. In the worldwide community where every organization strives to contribute, and this stage of profound globalization is unfolding. Organizations that do not adapt to diversity in its workplace will have difficulty staying competitive (Tamn et al., 2019). Over the past two decades, companies have appreciated employee diversity as crucial to economic sustainability (Shah et al., 2021). Diversity at the workspace is of priceless value, because it coalesces numerous latent capabilities and experiences, ultimately optimizing efficiency and effectiveness of the whole organization (Inegbedion and his colleagues, 2020).