Multiplication Rule for Independent Events

Multiplication Rule for Independent Events It is important to know how to calculate the probability of an event.  Certain types of events in probability are called independent.  When we have a pair of independent events, sometimes we may ask, What is the probability that both of these events occur?  In this situation, we can simply multiply our two  probabilities together. We will see how to utilize the multiplication rule for independent events.  After we have gone over the basics, we will see the details of a couple of calculations. Definition of Independent Events We begin with a definition of independent events.  In probability, two events are independent if the outcome of one event does not influence the outcome of the second event. A good example of a pair of independent events is when we roll a die and then flip a coin.  The number showing on the die has no effect on the coin that was tossed.  Therefore these two events are independent. An example of a pair of events that are not independent would be the gender of each baby in a set of twins.  If the twins are identical, then both of them will be male, or both of them would be female. Statement of the Multiplication Rule The multiplication rule for independent events relates the probabilities of two events to the probability that they both occur.  In order to use the rule, we need to have the probabilities of each of the independent events.  Given these events, the multiplication rule states the probability that both events occur is found by multiplying the probabilities of each event. Formula for the Multiplication Rule The multiplication rule is much easier to state and to work with when we use mathematical notation. Denote events A and B and the probabilities of each by P(A) and P(B). If A and B  are independent events, then: P(A and B) P(A) x P(B) Some versions of this formula use even more symbols.  Instead of the word and we can instead use the intersection symbol:  Ã¢Ë† ©. Sometimes this formula is used as the definition of independent events.  Events are independent if and only if P(A and B) P(A) x P(B). Example #1 of the Use of the Multiplication Rule We will see how to use the multiplication rule by looking at a few examples.  First suppose that we roll a six sided die and then flip a coin.  These two events are independent. The probability of rolling a 1 is 1/6. The probability of a head is 1/2. The probability of rolling a 1 and getting a head is 1/6 x 1/2 1/12. If we were inclined to be skeptical about this result, this example is small enough that all of the outcomes could be listed: {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)}.  We see that there are twelve outcomes, all of which are equally likely to occur.  Therefore the probability of 1 and a head is 1/12.  The multiplication rule was much more efficient because it did not require us to list our the entire sample space. Example #2 of the Use of the Multiplication Rule For the second example, suppose that we draw a card from a standard deck, replace this card, shuffle the deck and then draw again.  We then ask what is the probability that both cards are kings. Since we have drawn with replacement, these events are independent and the multiplication rule applies.   The probability of drawing a king for the first card is 1/13.  The probability for drawing a king on the second draw is 1/13.  The reason for this is that we are replacing the king that we drew from the first time.  Since these events are independent, we use the multiplication rule to see that the probability of drawing two kings is given by the following product 1/13 x 1/13 1/169. If we did not replace the king, then we would have a different situation in which the events would not be independent.  The probability of drawing a king on the second card would be influenced by the result of the first card.

Agustine and Aquina's justifications of the exercise of social and Essay

Agustine and Aquina's justifications of the exercise of social and political ruling - Essay Example ix). St. Thomas Aquinas was born in the early 13th century, of an affluent family, with direct blood lines to the ruling royal families of the day (Dyson, R.W., 2002, p. xvii). He began his religious training as an oblate, at the Benedictine monastery in Monte Cassino (p. xvii). Later, in 1245, became a member of the Dominican order, and furthered his education at the University of Paris where the German theologian Albertus Magnus introduced him to the study of Aristotle. In 1248 he followed Albertus to Cologne (p. xvii). It was earlier, however, while at the monastery, that Thomas studied Aristotle (p. xvii). Two great men, philosophers, separated by hundreds of years, whose interpretations and writings on political theory continue to influence the thinking of great men, women, religious, and political leaders today. This brief essay is an examination and comparison of the two schools of thought as they pertain to the governance of society socially and politically. The paper will rely on the works of St. Augustine, using his City of God as translated by Marcus D. D. Dodds (1950), and St. Thomas Aquinas’s Political Writings translated by R.W. Dyson (2002). To read either work without the benefit of a modern translation would be, at best, a slow and difficult endeavor that could perhaps, for some, take a lifetime. Under the guidance of the translators, we can gain a sense of the political ideologies of both Augustine and Aquinas. St. Augustine watched as the world around him spun out of control and into chaos, culminating with the fall of Rome, in 410 A.D (Dodds, p. ix). Rome’s fall brought crashing down the myths that Rome would last forever and rule the world (ix). It would have been a time when scholars, like Augustine, would be formulating thoughts and ideas, influenced by their philosophical teachings and interpretations, about world leadership and political and social manifestations of corruption and

International business management Assignment Example | Topics and Well Written Essays - 3000 words

International business management - Assignment Example 3- Socio-Cultural Factors: Majority of the organizations avoid introducing their products in the international market due to socio-cultural factors. Organizations fear that introducing any product or operating their business activities in a different culture with unusual traditions may risk their reputation and this could have an adverse affect on their potential growth. Therefore, it is important to know that it is the sound understanding of the social and cultural factors that distinguish the business operations of an international and domestic firm. Domestic firms possess better understanding of the social and cultural factors unlike an international firm which struggles hard to analyze and understand them. An international business may lose the business opportunity in the host country, if it fails to understand the local environment, behavior, attitudes and various other cultural factors. 4- Technological Factors: Technological factors play an important role in creating issues fo r an international firm to start their business activities in such a country that has little or no proper technological and communication infrastructure. This would increase the cost of producing or starting a venture in the host country. Differences between Domestic and International Strategy: Factors Domestic Conditions Global Conditions Culture Homogeneous Heterogeneous Currency Standard and uniform Different currencies and exchange rates Economy Stable and consistent Uncertain economical conditions Government Stable Unstable and uncertain Labor Easy availability of skilled workers Hard to find the skilled labors. Language Single Language Different languages with different dialects Marketing Many media, broad exposure and few restrictions. Fewer media, minimum... The paper tells that globalization has helped the economies to improve their trade, investment and how these economies can enhance their international businesses. There are different issues that a firm takes into an account before entering the global market. It is highly important for an organization to carefully analyze all the key issues and factors that can affect on the international operations before entering into global market. These key international issues are: economic forces; political and legal factors; socio-cultural factors and technological factors. Corporate social responsibility refers to the set of obligations on a firm for its approach towards social contribution in the society it operates. As we know that, multinational corporations operate in a culturally and socially diversified structure therefore, they are under more challenges to fulfill their share of corporate social responsibility in the country they are operating as compare to domestic/local firms. Multina tional corporations operate in the host country with the intention of benefiting the host country by bringing employment opportunities to them, giving boost to their economy and by introducing the latest technology in the country. However, there are certain factors that MNCs should consider while operating in any other country such as taking care of the corporate social responsibility which is an obligation to be fulfilled on all the MNCs. This is mainly due to the fact that these international businesses face more challenges as compare to domestic firms and local businesses.

brave new world :: essays research papers

In Brave New World, by Alduous Huxley, a new and controversial society is presented to its audience. A world of artificial intelligence where humans are cultivated in test tubes and social class is predetermined by the chemical mix they receive in vitro leads John Savage into corruption. He is torn between a world in which people’s fates were placed upon themselves and a world in which Alphas and Betas ruled a society with n identity. Thomas Mavin gives thorough insight into the classification of the two societies and favors the world of Malpais, a society that allows people to have control over their lives and experience true feelings instead of fake happiness. Between these two worlds with different positions on free will, the only way for people to live a truly meaningful life would be to live in Malpais.   Ã‚  Ã‚  Ã‚  Ã‚  In the Brave New World, Huxley created a society in which people acted upon the cast they were born in. There was no such thing as free will and happiness could be purchased in a pill, soma. In fact, Arthur Cross wrote in A Shorter History of England and Greater Britain that â€Å"In Brave New World, there’s pleasure as a substitute for freedom.† In this world, people would rather become blind to the truth of life by forcing themselves into a â€Å"high† instead of dealing with the facts of life. With this pill, people are able to take themselves away from stressful, depressing, or uncomfortable moments of life. They become oblivious to true life. In fact, to many of they characters who constantly use the pill, their lives become dreams because often they are not truly living in it. Cross also points out that the Brave New World was more stable and well maintained because of conformity and single points of views. In the society today, there is the constant threat of wars and altercations with different people or countries. With a uniform society, comes uniform ideas and peace. With this in mind, countries save millions of dollars because there is no need for weapons of mass destruction. This new society becomes thoroughly efficient. There is only one leader, the World Leader, and the people live under his iron- clad fist. With the Democratic Party and Republican Party in today’s society comes constant conflict and there is always one side that will be unpleased with certain decisions and laws.

A Note on the Cuban Cigar Industry – 1

â€Å"A Note on the Cuban Cigar Industry† 1. Threats of new entrants: Product differentiation is major player in the market of Cuban Cigars, with certain brands being linked to prestige and honor. Also, restrictions from the world make it difficult for new entrants, because of trade embargos put in place by a majority of the most powerful countries in the world, including the United States. Power of suppliers: Cigar industry is dominated by two major suppliers, Altadis and Swedish Match, which control the distribution of Havana cigars and Cuban branded names, with Altadis being the largest cigar company in the world.Power of buyers: Buyers are willing to pay premium price for quality cigars, therefore, the power of the buyer is very minimal, as cigar enthusiast have increased worldwide. Threats of substitutes: The threat of substitutes is higher, where the actual tobacco seed has been farmed in locations outside of Cuba, including the United States, Dominican Republic, and Hon duras. As noted in the Case, 250 million cigars were exported to the United States from the Dominican Republic. Competitive Rivalry: Rivalry in the Cuban cigar industry is extremely high, where the industry growth has tapered off because of intense competition.Projections were high in the nineties for Cuban Cigar imports; however, with the fear of loss in quality and exclusivity of the cigars, the projections were lessened. Even though there has been a steady increase in exports, it has not been heavy, exhibiting the fact that there are few â€Å"real† producers of Cuban cigars. 2. Given the previous analysis, based on Porter’s Five Forces model, I would without a question invest in the Cuban cigar industry. For a few decades now, the industry has been on the rise, with cigar connoisseurs always remaining loyal and faithful to their preferred brands of cigars.At first, the tobacco firms were increasing their production rapidly, all the while trying to maintain and impr ove quality, however, that was too difficult of a task, so in turn, Ana Lopez, the head marketer for Habanos S. A. changed their focus and decided to keep working at improving quality at any expense. The quality remains, and with that remains a set group of cigar buyers, who would rarely stray from a brand that they have become affixed to. Specifically, I would target my investments towards the distributors of the cigars, as they not only supply Havana or Cuban cigars to the world, but also many other popular brands and types.The main barriers that exist in investing in the Cuban Cigar industry are the U. S. trade embargo as well as the type of government ruling over Cuba, Communist. The trade embargo puts a huge blemish on Cuban cigar export numbers, where the numbers could be increasingly high. Furthermore, because of the Communist government in place, it isn’t always easy for competitors to start new ventures, or to keep profits on the rise. 3. My decision would remain the same; I would still invest in the Cuban cigar industry, even if the trade embargo is lifted.However, the difference in the analysis comes in the situations of rivalry, new entrants and power of the buyers. All of these would change completely with trade being allowed to the United States, who stakes claim to more than 500million premium cigar imports a year, of which, zero are â€Å"officially† Cuban cigars. If the U. S. were to lay stake in the Cuban cigar industry, the entire market would be revamped, with competitors springing up everywhere, buyers gaining more control, and competitive rivalry going on the rise.

Analysis Of Death Of A Salesman - 1859 Words

In â€Å"Death of a Salesman†, Willy and his family live in post-war Brooklyn, where America was enjoying a state of economic prosperity. In an attempt to shield Americans from the influences of communist ideals, Americans felt that financial success supported a capitalist society. The American dream is the belief that any American citizen can achieve their dreams if they are hard working, even those who are destitute. This idea of equality is criticized by both of the texts I will be comparing. In this essay, I will be exploring the author s portrayal of the American Dream and how it leads to the inevitable destruction of society. I will discuss how the pursuit of the American dream can lead to problems within characters relationships. In the play â€Å"Death of a Salesman† Willy holds a strongly deluded belief in the American Dream, which leads to his mental instability. We can see this when he says â€Å"Suddenly I realize I’m goin’ sixty miles an hour and I don’t remember the last five minutes.† Willy is both delusional and contradictory. Willy contradicts himself every time he talks, saying â€Å"Biff is a lazy bum!† then â€Å"There’s one thing about Biff — he’s not lazy.† This contradiction shows us that Willy is confused and that he may be only expressing a different opinion as to what he actually believes, hiding his true feelings. In this case, Willy holds onto the hope that maybe one day Biff will not be lazy and that Biff can live up to his father’s expectations of becoming richShow MoreRelatedDeath Of A Salesman Analysis914 Words   |  4 PagesLies of a Salesman (Movie Analysis of Death of a Salesman produced by Robert F. Colesberry) To be dysfunctional is to not operate accordly to normal in a negative way. Death of a Salesman produced by Robert F. Colesberry is a movie based on a play Death of a salesman written by Arthur Miller. The Loman family in the movie is a dysfunctional family, which is clearly show in many scenes,The mother and the father Willy and Linda Lowman. Willy a salesman in the field for over 30 years. The have kidsRead MoreAnalysis Of Death Of A Salesman 900 Words   |  4 PagesCritical Essay In Arthur Millers â€Å"Death of a salesman† we encounter an on-going feud between salesman Willy Loman and his son Biff Loman. In Willy’s eyes the key to gaining success in life is to be well liked, attractive and having a great personality, he is convinced if you have all these traits it guarantees you success and that you could outrun those with qualifications in terms of being employed. Willy bestows this theory of his onto his sons Biff and Happy during their teenage years. DuringRead MoreDeath of a Salesman Analysis675 Words   |  3 PagesNovember 10, 2012 English P5 Death of a Salesman Essay Like Father Like Son In Arthur Miller’s play, Death of a Salesman, Miller reveals what happens when a dream, especially the American dream, dies, as seen through the life of Willy Loman, a pathetic, self-deluded salesman. The play follows the family through painful conflicts, significant issues such as national values, and the price of blind fate while working toward the ‘American Dream’. The major problem woven into the plot discussesRead MoreDeath Of A Salesman Analysis1351 Words   |  6 PagesIn Arthur Miller’s, Death of a Salesman, Biff Loman confesses the following to his brother, Happy: â€Å"I don’t know—what I’m supposed to want† (22). Biff is expressing his internal struggle between wanting to live up to his father’s expectations and his desire to pursue what he really wants-- to be outdoors. Biff is conflicted and views himself as a failure for not achieving his father’s image of success. At the end of the play, Biff realiz es that in order for him to be truly successful he has to stopRead MoreDeath Of A Salesman Symbolism Analysis1145 Words   |  5 PagesSymbols in â€Å"Death of a Salesman† by Arthur Miller Symbolism, as defined by Oxford Dictionary, is the â€Å"use of symbols to represent ideas or qualities.† Throughout the play Death of a Salesman, by Arthur Miller, he uses symbols to represent a greater idea and to say more than what is actually being said. Through the use of silk stockings, a rubber hose, and the flute music that drifts through the play, Miller demonstrates the power that these items have over the Loman family. One reoccurring symbolRead MoreAnalysis Of The Play Death Of A Salesman 954 Words   |  4 Pages Darrian Dowden AP English IV Death of a Salesman Written Assignment Death of a Salesman Character Analysis 1.Willy Loman. Although the main protagonist of the play, Willy Loman does not come to a certain self-realization. Searching and sifting through his memories (which cannot be completely taken as the truth as he reinvents them in a way to make them out as a golden era) he fails to recognize his slanted reality he’s lived in made up of his delusions. His forged relationship withRead MoreDeath of a Salesman Analysis Essay2107 Words   |  9 Pagesfamily; however, there has been much debate over whether or not the American dream is still obtainable in modern society. One piece of American literature that substantiates the fact that the American Dream can not be gotten is Arthur Miller’s Death of a Salesman which describes the tragedy of the average person in America. A number of other writers also draw the inability to capture the American Dream. John Steinbeck demonstrates in his highly acclaimed novel The Grapes of Wrath how hard economic timesRead MoreAnalysis of the Ending of De ath of a Salesman1261 Words   |  6 PagesAnalysis of the Ending of Death of a Salesman The play Death of a Salesman shows the final demise of Willy Loman, a sixty- year-old salesman in the America of the 1940s, who has deluded himself all his life about being a big success in the business world. It also portrays his wife Linda, who plays along nicely with his lies and tells him what he wants to hear, out of compassion. The book describes the last day of his life, but there are frequent flashbacks in which Willy relives key eventsRead MoreAnalysis of Biff in Death of a Salesman Essay1584 Words   |  7 PagesCamilla Tanzi Year 12 An analysis of the character of Biff. Biff Loman is portrayed as the root of Willy’s mental illness and instability. He is also the only member of his family who acknowledges his own failures in life. On the whole, Biff Loman stands out as the most intriguing and strong character in â€Å"Death of a Salesman. He is not a successful man and never will be, he is however able to admit this, even in a harsh society as the one of the 1960s America. Biff knows he is a â€Å"nothing† andRead MoreA Detailed Analysis of Death of a Salesman1199 Words   |  5 PagesLook at Death of a Salesman Death of a Salesman has been accepted worldwide as one of the greatest American dramas to premier in theatre. The story behind the play is based on Miller’s interactions with his Uncle, a salesman whose efforts to obtain the â€Å"American Dream† and pass his success on to his two sons becomes his main focus. Miller’s life during the preparation of Death of a Salesman provides the spark and inspiration needed to pen a literary classic. Almost five decades later, Death of a Salesman’s

Essay on The American Dream in The Jungle by Upton...

Muckraking, â€Å"to search for and expose real or alleged corruption, scandal, or the like, especially in politics† (dictionary.com). Upton Sinclair gained fame in the early 1900’s from his muckraking novel, The Jungle, describing the life of a young Lithuanian immigrant, Jurgis, living in Chicago in pursuit of the American dream. Jurgis found out that America isn’t as good as it appeared; with higher wages came more expensive goods, and with cheaper houses came higher interest rates. The Jungle, a fictional novel, tells of the real horrors of working in a Chicago meat packing factory. Sinclair had gone undercover, in a meat factory, for seven weeks to gain the information necessary to write the book. Throughout the novel, there are hints of†¦show more content†¦Rockefeller, Andrew Carnegie, Henry Ford, Cornelius Vanderbilt, and JP Morgan along with the formation of unions. The Jungle, from 1906, has been deemed as â€Å"a classic denunciation of indus trial capitalism and one of the most revolutionary novels of the age† (wordsocialism.org). In the â€Å"Progressive Era†, Sinclair’s ideas were at the center of the social movement, due to the brutality of the time period, The Jungle was not easily published. â€Å"The aesthetics of a novel include the way an author uses elements of style, such as imagery, irony, and paradox, to enhance characters, plot, and theme. From this perspective, The Jungle is not considered quality literature.† (cliffsnotes.com) Others thought that Sinclair only wrote the novel as propaganda for his political career, or as a simple muckraking novel. He was not thought to write nonfiction, so his words could not always be trusted. For these reasons, Sinclair was not considered a serious author. Sinclair was an expressive socialist, and showed his beliefs in his novels. In The Jungle, Sinclair frequently referenced socialism and how it would fix all the problems created through capitalism. â€Å"Capitalism is not the problem.Show MoreRelatedMy Favorite Book is The Jungle by Upton Sinclai610 Words   |  2 Pagesimpressed me as The Jungle by Upton Sinclair. To me this book is one of the finest books in the world. In fact this novel is so remarkable that it made history and changed the course of events. The Jungle’s excellent qualities have made it my favorite book. Upton Sinclair’s The Jungle was first published in the United States in 1906. This book became an immediate success as it portrayed the corruption within American business and government. Sinclair based the novel on the American meatpacking industryRead MoreThe Jungle by Upton Sinclair: Fame for the Wrong Reason Essay2798 Words   |  12 Pages1900’s America begin to transform rapidly. Many immigrants started moving to the United States in the early 1900’s with the hopes of living the â€Å"American Dream.† However, that glittering and gleaming American lifestyle is merely a distant ideal for the immigrants living in Packingtown, the meatpacking district of Chicago. Upton Sinclair’s The Jungle portrays life through the eyes of a poor workingman struggling to survive in this cruel, tumultuous environment, where the desire for profit amongRead MoreBrief Survey of American Literature3339 Words   |  14 PagesBrief Survey of American Literature 1. Beginnings to 1700 Great mixing of peoples from the whole Atlantic basin Bloody conflicts between Native Americans (or American Indians) and European explorers and settlers who had both religious and territorial aspirations - Native American oral literature / oral tradition - European explorers’ letters, diaries, reports, etc., such as Christopher Columbus’s letters about his voyage to the â€Å"New world†. - Anglo (New England) settlers’ books, sermonsRead MoreAmerican History Eoc Study Guide5327 Words   |  22 PagesAmerican History EOC Study Guide 1) Reconstruction: A plan to reconstruct the society after the Civil War. This divided the south (except Tennessee) into 5 military districts under the control of the U.S. Army. It was the attempt to reconstruct the south, readmit the southern states back into the Union, and change the life of African Americans. (pg. 414) 2) Freedman’s Bureau: Congress created this in March of 1865 in order to provide help for thousands of poor black and white southernersRead MoreFeminine Mystique12173 Words   |  49 Pageshappened? When did women decide to give up the world and go back home? Friedan asked herself. Questions like those have engaged historians since the 1970s, but they were not ones housewives of the 1950s were encouraged to ask. For a red-blooded American to doubt something as sacred as the role of housewife and mother was to show symptoms of mental disorder rather than a skeptical or inquiring mind. Whatever the label attached to such feelings — neurosis, anxiety, or depression — most people assumed