Post and 2 responses Explain how the concepts of probability theory can give rise to puzzle and paradox Explain why we cannot trust our intuition with probability and yet 99% of the decisions we make in no technical environments are made with the benefits of human experience and intuition. POST 1 1st:The goal of probability theory is to formalize randomness and chance into a mathematical equation (Sharma, J.K, 2006).  A paradox is an outcome that is subject to controversy, rupture and different beginnings that contradict your baseline knowledge according to Borovcnik (Borovcnik, M., & Kapadia, R., 2014).A puzzle is a solution that is intuitively not in line with our preconception of the idea (Borovcnik, M., & Kapadia, R., 2014).  The probability theory is the theory that random outcomes cannot be predicted before they occur.  In probability theory there is regularity but never exact predictions of outcome.People generally do not use mathematics in their everyday decision making process.  A lot of the time math is considered a “technical tool” when making decisions and 99% of decision making is done outside of that “technical environment” (Winkler, 1996).  Intuition is an important part of everyday life and everyday decision making, it can help steer you in the right direction but unfortunately intuition can come up short in some ways when it comes to making decisions based on data.  Our shortcomings in this area are from flaws that preexist in our minds.  According to Nobel winning economist Daniel Kahneman humans have two systems of thought.  System one is fast and intuitive and system two is slow and relies on reasoning (Borovcnik, M., & Kapadia, R., 2014). By using a combination of intuition and reasoning based on statistical information you can make quick decisions based on data that are fairly intuitive and accurate when applied correctly.Works CitedSharma, J. K. (2006). In Business Statistics, Second Edition. book, Pearson India.Winkler , P. (1996)  Probability and Intuition retrieved from https://ww2.amstat.org/mam/96/resources/winkler.html POST 2 2nd:The concepts of probability can give rise to puzzles and paradoxes ("birth of probability," 2021). The number of an event's outcome divided by the possible outcomes is what gives classical probability. The possible results are based purely on the uncertainty that adopts the principles of counterintuitive and contradiction, which leads to the rose of paradoxes and puzzles, respectively. The existing distinction between combinations and permutations and the related game theory are interconnected. In statistics, the puzzles and paradoxes are developed into mathematical concepts in the mathematics theories and practical. The probability and the related factors are explained as the likelihood's chance that a particular event will occur. Russell's most famous paradox discusses contradictions in the world when calculating probability and statistics ("birth of probability," 2021). Probabilities can be explained as proportions that range from 0 to 1 and are expressed in percentages from 0% to 100%. All the research-related activities are described as combinations and permutations.Intuitions are based on a gut level, and using impulses to make whatever decision would be based entirely on our judgments (Schreiber & Romero, 2021). Human beings develop heuristics in which they create a perception of the world, and that is why it would be challenging to use intuitions to make decisions. It is rather not advisable to do so. People who use their intuition to make decisions need to attribute to their surroundings, including their values, surroundings, and personal characteristics (Whittle, 2020). We cannot trust our intuition because most of our false intuitions are related to heuristics and other relatable concepts. Human behavior has evolved through the process of natural selection as well as the influence of genetics. Since intuition is affected by many different things, it might not always give the best judgment in all situations.ReferencesThe birth of probability. (2021). Chance, Logic and Intuition, 83-106. doi:10.1142/9789811229190_0004Schreiber, I., & Romero, B. (2021). Probability and human intuition. Game Balance, 491-508. doi:10.1201/9781315156422-20Whittle, P. (2020). Uncertainty, intuition, and expectation. Springer Texts in Statistics, 1-12. doi:10.1007/978-1-4612-0509-8_1

Rosemary, however, still felt unsure of herself and often isolated. There have been times that she was the only registered nurse on the unit all night. The aides and LPNs were very experienced, but Rosemary feels she is not ready for that kind of responsibility. Rosemary knows she must speak to the nurse manager about this, but she's called several times, and she's never available. The shift assignments are left in the staff lounge by an assistant. Questions Your discussion post should answer the following questions in a well-constructed commentary.  To what extent is this problem due to a failure to lead? Who has failed to act? What style of leadership was displayed by Rosemary? The nurse manager? How effective was their leadership? What are your suggestions for Rosemary?

In the following scenario, place yourself in the role of a newly promoted first-line supervisor (sergeant) at a police department. You will write a memorandum to the deputy police chief regarding the following scenario and what actions you will take to address the issues you identify. You have become aware that some officers in the department are using their badge and identification to receive free or discounted food and drinks at various establishments in and near your community. There are rules and regulations that regulate and prohibit officers from using their official capacity as police officers for financial gain. However, you are also aware that this is a long-standing practice and is widespread across the department including some officers in command positions. There have been no complaints from the public that have been brought forward that you are aware of, but you believe that this ethical problem undermines the reputation of the department and its officers. In a memorandum please address the following critical elements. 1. Identify the ethical dilemma presented. 2. What implications may this have on the police department as a whole? 3. What ethical concerns are there for the community in this situation? Why is it important to address this issue? 4. Propose how you would deal with this situation and what preventive steps you would take to ensure this does not occur again. 5. Articulate how the preventive steps you would take impact the performance of the police officers and improve their ability to address the problem and work more effectively. 6. Be sure to support your answer with scholarly evidence from the text or outside sources. You use can the Memorandum Template below to format your submission.