Mathematical Exploration
Probability and the Exploration of the Monty Hall Problem
Candidate Name: Tomass Pildegovičs
Candidate Number: 001001-0022
School Name: Riga State Gymnasium No. 1
Exam Session: May 2015
Table of Contents
Introduction 2
Solving the standard Monty Hall Problem 3
Solving modified versions of the Monty Hall Problem 4 Solving Fundamentally altering the conditions of the problem
Possible applications 9
Conclusion 9
Introduction
Monty Hall’s television game show Let’s Make a Deal gained widespread popularity in the 1960s and 1970s amongst the American audience. The set of this show would become the basis of one of the
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This claim was met with much controversy, as thousands of academics sent letters in which they voiced their staunch disagreement and accused vos Savant of propagating mathematical fallacy. Her answer -- that the contestant should switch doors -- has been debated in the halls of the Central Intelligence Agency and the barracks of fighter pilots in the Persian Gulf. It has been analyzed by mathematicians at the Massachusetts Institute of Technology and computer programmers at Los Alamos National Laboratory in New Mexico. It has been tested in classes from second grade to graduate level at more than 1,000 schools across the country. The correct solution to The Monty Hall Problem is to such a great extent counterintuitive, that it can be difficult to believe; yet it remains unwaveringly true. The aim of this investigation is to examine the solutions to this legendary problem in order to establish a general pattern, while exploring numerous variations of the original problem.
Solving the standard Monty Hall Problem
In order to attempt to solve the Monty Hall Problem, it is necessary to establish four key assumptions: The participant is attempting to win the car, not the goats. The host must always offer the chance to switch between the originally chosen door and the remaining closed door. The host must always open a door that was not first chosen by the
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Solving modified versions of the Monty Hall Problem
What if the set of the show had 4 doors?
There are now four doors to choose from, with one of the doors concealing a car and the other three doors concealing goats. The same four previously established key conditions still hold true.
Door 1 Door 2 Door 3 Door 4
Once again the participant has two options available: to stay with the first choice or to switch once the host has revealed one of the doors concealing a goat.
Option 1: Participant decides to stick with the initial choice. As there are 4 doors and only one of them conceals a car, the probability that it is the initially chosen door is p(x)=1/4 or 25%. Just as in the case with 3 doors the probability of the car being behind the initially chosen door does not change over the course of the
The stories The Lottery by Shirley Jackson and The Rocking-Horse Winner by D.H. Lawrence share similarities in their stories. The difference is based on the three major areas in examining any story which are the character, plot, and setting. In general, the atmosphere is configured so that readers are attracted to fiction. A brief prose tale that can be read in one sitting, usually plot function as the driving force. The writer allows the reader to have a complete view of the story, based on the configuration.
He begins his article by talking about the small chance people have in winning the lottery. Most of the article describes Piore’s interactions with Hargrove, the Lottery legend. He explains that Hargrove “built the state lotteries in Georgia and Florida from scratch” (Piore 700). He also talks about the legend’s expertise in the business of lottery and her “intuitive understanding of what drives her customers to play the game” (Piore 700). The author’s interaction with Hargrove gave him more insight and understanding of the tricks and logical manipulation of human brain in believing what is not factual.
Many people would die to win the lottery; in the short story “The Lottery” by Shirley Jackson you would do anything NOT to win this lottery. This annual lottery reveals the negative aspects of this town’s Tradition, Savagery, Barbarism, and cold-heartedness. In this paper I will show why this town blindly follows these customs, not because it’s a tradition but because of the accepting wickedness that can be shown. Why does the town follow this foolish tradition? Throughout “The Lottery” the narrator tells that the people do not remember how the lottery began, and that some of the older people believe the lottery has changed over the years, that now people just want to get it over with as fast as possible.
A time in history that holds significance in ‘The Lottery’ is the red scare. During the late 1930s and 1940s, the citizens and the government of the United States were increasingly paranoid of a communist uprising, and the presence of Soviet spies. This came to be known as the red scare, and this paranoia lead to the destruction of many lives and professional careers. A significant number of people experienced their reputations being tarnished, and individuals were jailed for having, or simply being accused of sharing communist beliefs. Subsequently, many members in society were quick to divert attention from themselves, and in turn offer the names of friends and neighbours to the authorities.
A tradition or idea that is followed and not questioned by some could potentially be dangerous or illogical. In Shirley Jackson’s short story “The Lottery”, the dangers of blindly following a tradition is portrayed. In “The Lottery,” a village gathers around every year on June 27th to hold a lottery. Mr. Summers leads the tradition every year. This lottery is very unusual; the winner will become the loser.
Although, Holcomb is written as a picture-esque mid-west utopia in the first chapter of In Cold Blood, Capote uses personification, parallelism, and the inclusion of first hand accounts, to describe its shift from a neighborly society to one of locked doors in order to comment on how one event can completely alter a locations image. Through the use of personification, Capote describes the disillusion in the townspeople of Holcomb, product of the murder of the Clutter family. Capote writes that locks and bolts are the most popular item in a Garden City hardware store, and that the people disregarded brand identity just to have the security of the ownership of a lock. Capote latter writes, “Imagination, of course, can open any door - turn the key and let terror walk right in” (Capote 88), to show how paranoia has consumed the townsfolk are by expressing the false sense of security that a door lock provides. The use of “imagination can open any door”, implies that if someone needed to get through a locked door,
Research Paper The famous short story by Shirley Jackson "The Lottery'" was published on June 26th, 1948. The short story has been drawn into discussion for many years for its short, but intricate and complex story. A summary story in its simplest form could be put as a tradition that was followed by a small town called the lottery, but there is so much more contained in between the lines of that statement. The story has a very dark premise regarding the tradition that the town must follow is for the safety of the town itself.
The story of “ The Lottery ” by Shirley Jackson is a very surprising story especially towards the end. It causes great consternation and shock when we learn that the winner of the lottery - Tessie Hutchinson, does not win an award, rather finds herself stoned to death. This somewhat shows the role that superstition played years ago. It was widely prevalent and as we progressed in terms of science and technology, we have come to break apart from such harmful traditions. It is precisely due to these superstitions, often many an innocent life has been taken without just cause.
Diverse Competitors Desperate to Find Halliday’s Easter Egg Have you ever been really invested in a video game, quest, contest, or something that promises a rewarding win? The competitors vying for the large fortune that comes with winning James Halliday’s Easter Egg Hunt sure are. Throughout the virtual reality that is the OASIS, the goal is to capture the several keys Halliday has strategically placed around the OASIS to eventually discover his special hidden egg, leading to a desirable win of fame and fortune. The stakes are high when we consider the fact that many players have invested years in a quest they may be unsuccessful in. On the flip side, though, there is a lot of potential gain with the promise of winning a large fortune for
Throughout centuries, traditions and rituals have had the ability to control one’s behavior. In Shirley Jackson’s, “The Lottery”, she tells the reader of a small village. On the surface, this community may seem relatively normal. However, despite the picturesque appeal, this falsely serene village has a distinct deceitful flaw. On June 27th, every year, a lottery takes place.
The short story “The Lottery” written by Shirley Jackson, the plot in the story that it only gives people an account of drawing lots to determine the winner who shall be stoned to death for harvest. However, we get a deep impression of the characters and their fate after reading the story. Jackson indicated a prevalent theme, the indirect of characterization and using symbolism and irony to modify this horror story. The Allegorical story of “ The Lottery” is often regarded as a satire of human behavior and social institutions, and exemplifies some of the central themes of Jackson’s fiction, including the victimization of the individual by society, the tendency of people to be cruel, and the presence of evil in everyday life.
Trolley problem, initiated by Philippa Foot, is a situation in which there is a runaway trolley and the only way to save five people on the tracks is to sacrifice one person (Kvalnes, 2015). There are many versions of the trolley problem with regard to how the one should be sacrificed, make trade-offs in order for five persons to be saved. In this paper, there are two trolley case used to compare with the autonomous car case. The first case, called the switch case, come from Philippa Foot (1967), in which there is a third person who are standing next to a signal switch.
The Lottery is one of Shirley Jackson’s masterpiece. She was born in California, graduated from Syracuse University in New York and was successful in writing novels, short stories, children’s fiction and biographies. In this short story, Jackson showed uncommon and absurd events in common settings that when it was published, many of the readers asked her questions as to how the conclusion was interpreted. In this analysis, Formalistic approach is the approach used.
But what one learns later on in the story is that this warm summer day being explained is the day of the lottery. The lottery is conducted by Mr. summers, he prepares the slips the night before and gets the black box all ready for the following day. As everyone is getting ready to meet at the
In Orwell’s novel 1984, Room 101 represents the power of the Party and is the room where Winstons spirit is crushed. Room 101 is a presentation utilized by the party to show absolute dominance. It proves that the party has the power to totally ruin someone through the use of their deepest fear. Fear is the ultimate dominance. If you can purchase the power to pressure someone to meet their biggest fear, you have the ultimate dominance over that individual.