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.

Equality, Freedom, And Religion Essay - 2571 Words

In the book ‘Equality, Freedom, Religion,’ Roger Trigg discusses concepts surrounding freedom of religion, freedom of beliefs and equality. In particular, he discusses the idea of religious freedom and how courts and the law should observe the religious beliefs and practices of a person. This essay will provide a critical analysis and review of several major points in the text, firstly, the idea of religious freedom as a human right will be critically discussed as it is a concept that is important for the whole book. Secondly, religious freedom and equality will be discussed with reference to religious beliefs and non-religious beliefs. Thirdly, innate religious belief will be discussed as a potential factor for the argument that religion may deserve more protection over general beliefs. Next, the sincerity of religious beliefs will be analyzed with reference to court rulings. Additionally, equality between beliefs will be critically discussed in particular regarding la ws and cases in America. Finally, an overall personal opinion of the text will be provided and discussed by the author of this essay. Firstly, Trigg presents the concept of religious freedom as a human right in the introduction of the text, this concept is integral for the rest of the subjects discussed by Trigg in the book, for the reason that, the rest of the book recognizes the freedom of religion as a human right. The idea that religious freedom is a human right is particularly important when TriggShow MoreRelatedPresident Obama Addressed The Nation s Problem Of Inequality1398 Words   |  6 PagesIn his 2013 Inaugural Address, President Barack Obama addressed the nation’s problem of inequality people are faced with each and everyday day and how these inequalities affect the concept of freedom. 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George Washington states in his Rules of Civility, â€Å"When you speak of God or his attributes, let it be seriously, in reverence andRead MoreThe Role Of Values And The National Identity916 Words   |  4 Pages The Role of Values in the National Identity Do you imagine we can identify the Americans’ national identity, via their religion, ethnicity, language, or civil war? There are a lot of countries around the world their religion, ethnicity, or language symbolized to their identity. Such as, Kingdom of Saudi Arabia, or Islamic Republic of Iran. However, the Americans are considered as a unique society, because the cultural pluralism which has been influencing their lives in the various aspectsRead MoreDifferent Opinions Can Colide Essay737 Words   |  3 Pagescitizens and slaves of the United States expected ideal changes that would affect their way of living. Most of the beliefs people had consisted of liberty, equality and religion. 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International Classification of Accounting Systems Free Essays

string(40) " on the American stock exchange places\." Classification of Accounting Systems Critically evaluate to what extent past research into classification of accounting systems has become irrelevant because of international harmonization efforts. Let us remind that IASC was replaced in 2001 by IASB (International Accounting Standards Board). We are going to start this paper with the different classification researches, taking for example Hofstede and Gray’s studies. We will write a custom essay sample on International Classification of Accounting Systems or any similar topic only for you Order Now Then we will draw the main differences between GAAP (Generally Accepted Accounting Principles) and IFRS (International Financial Reporting Standards). We will also speak about the Americanocentrism problem. To finally dealing with the differences and harmonization. *Two Main Example*s* of Past Studies*: *Hofstede’s* societal dimensions and Gray’s accounting values Different Classification Researches The first one is the deductive or judgmental method. Environmental factors are identified and they are linked to national accounting practices. Then, international groupings and development patterns are proposed. The second one is the inductive or empirical approach where individual practices are analyzed; the grouping or development patterns are identified, and where the explanations are based on economic, social, political and cultural factors proposed. In the deductive approach, Mueller developed four approaches to accounting development. Macroeconomic pattern: where business accounting is tied to national economic policies (Sweden, France, Germany) Microeconomic pattern: where accounting is a branch of business economics (Holand) Independent discipline pattern: where accounting is a service function derived from business practices (US, UK) and where accounting is considered to be capable of developing its own conceptual framework from business practice. Uniform Accounting pattern: where accounting is an efficient mean of control and administration. It takes into account that culture and historical roots are very important. Hofstede define four societal dimensions: individualism versus collectivism, large versus small power distance, uncertainty avoidance: degree to which a firm is ok with ambiguity, masculinity: preference for achievement, assertiveness, material success. Now let us focus on Gray who has developed the following pairs of contrasting accounting values: Professionalism VS Statutory Control: there is a preference for individual judgment, self regulation. Uniformity VS flexibility: there is a preference for enforcement of uniform practices. Conservatism VS Optimism: there is a preference for cautious approach. Secrecy VS Transparency: there is a preference for confidentiality. There are a lot of international pressures like the growing international interdependencies and the harmonization of the regulatory framework. But also the new opportunities, joint ventures and alliances. *GAAP/*IFRS Let us start by an analysis of the GAAP (Generally Accepted Accounting Principles). Financial accounting relies on certain standards of the GAAP. Principles of GAAP derive from tradition. There are seven main principles: regularity or consistency, sincerity, permanence of methods, non compensation, prudence, continuity, and periodicity. In any report of financial statements (audit, compilation, or review), the auditor must indicate to the reader whether or not the information contained within the statements complies with GAAP. The convergence of accounting standards, that the majority of the industrialized countries support is advantageous for the companies in the Stock Exchange: they should not have to produce several financial statements and thus save important sums of money. The financial risk is reduced. The investors, for their part, can better compare and examine the financial data of companies wherever they are established. Their decision making is thus improved. This international harmonization is a process making it possible to arrive to a basic bringing together various accounting standards One big advantage can be seen when we face a merger or an acquisition. Decisions are much easier to take. However, the experience of convergence IASB/FASB shows that many years are necessary to ensure the convergence of two reference frames however based on the same Anglo-Saxon culture of the businesses. This is due primarily to an existence of an opposition between an approach by the rules in the case of FASB and an approach by the principles which follows IASB. IASB is at the center of the convergence movement. The IFRS are described like founded on principles, which means that they leave a big freedom of action to the companies about the evaluation of the accounting data. The US GAAP are described like founded on rules and they aim to regulate all the possible aspects of the presentation of the accounts. These standards thus require very detailed information on behalf of the companies. In the case of convergence between IASB and FASB, the harmonization of the IFRS and US GAAP is currently working and common solutions have already been found. That do not prevent from the divergence of several points of view, among the principal aspects to be solved one we think about the financial instruments and the presentation of the performances. Some of the differences between US GAAP and IFRS are embodied in the standards themselves. They are intentional deviations from US requirements. Americanocentrism Some countries adopted some international standards coming to replace their national standards or to supplement them. Some stock exchange places, first of all the London one, admitted companies of which accountancy is in conformity with standards IAS and more than 200 great groups (majority domiciled in Canada, in France and Switzerland) produced a second set of accounts established according to these standards. SEC even conceded at certain foreign companies the right to observe certain rules IAS as the standard relating to the table of financing (IAS 7), to currencies (IAS 21), companies (IAS 22) and inflation effects (IAS 29). Within the European Union, some harmonization efforts about accounting methods were undertaken. Those however knew the same fate than others and must still produce tangible effects. Moreover, European countries have adopted the principle of mutual recognition of the standards. In spite of the creation of an ad hoc work group in 1990, the accounting harmonization is not a priority anymore, no proposal nor declaration has been made since. It is use consider American standards as the reference. That does not imply their superiority that just reflects economic and political reality. Unless standards IAS are not accepted by the SEC, the companies which follow them do not meet the conditions to be allowed on the American stock exchange places. You read "International Classification of Accounting Systems" in category "Papers" To be allowed, a German group like Daimler-Benz must satisfy the regulations and specifications of the Stock Exchange where its shares will be exchanged and to match the regulations imposed by the SEC, slightly amended for the foreign transmitters. SEC requires in particular that foreign companies present either their accounts in conformity with the US GAAP or a table showing together the US GAAP rules and the accounts drawn according to the accounts chart of their own country (Germany in the case of Daimler-Benz). Few companies choose the first method; nevertheless, even the second method is expensive. If the American Stock Exchange remains one of the more world significant markets, standards IAS non in conformity with the American rules will become obsolete. But if the SEC persists in its exclusive attitude, the domination of the American Stock Exchanges could be compromised. Can we solve the problem? Is harmonization the answer? Then harmonization in accounting standards shall serve many of the following benefits: Decrease in the costs of data collection Increase in the comparison of the information, Development in the capital markets, Facilitation in the fund movements Provision of competition advantage in favor of the firms Decrease in the audit costs and increase in the efficiency of the audit For multinationals, the advantages of harmonization are much more important. The impacts are cultural and social, on the employment and consumption pattern for example which are significantly influenced. The SEC made understand that any international reference moving away from philosophy and specificity of the American standards would not be acceptable. It profits from the support of Financial Accounting Standards Board (FASB), insofar as generalized acceptance of standards IAS could compromise the credibility of standards FASB. *Why do the differences persist? And w*hat is *mainly *stopping* the harmonization*? Let us take another example. In Japan, Keiretsu is a group of companies undertaken with cross participations which maintain very close relations of customer-suppliers type. Similar systems exist in Korea. The relations between these companies are not comparable with those which bind a holding and its subsidiary companies; this system is running in United Kingdom and the United States. Moreover, no economic argument could be brought to justify the regulation of the accounting standards. Why the practices differ o clearly from one country to another? We can for sure think about culture, tradition and history. Then, external environment, legal systems (Common law Codified Roman law), taxation, the level of inflation, accidents and external influences (such as the framing of law in response to economic or politic events for example) are the main causes of international differences. Also, liabilities, consolidation, segment reporting and foreign currency translation can be big issues in international accounting. However, the economists privilege the explanations relating to factors such as the legal system and the legislation on the property rights, even if, in the final analysis, these factors themselves form part of each culture intrinsically. Conclusion While convergence and harmonization are admirable goals with a lot of benefits, that may not easily or quickly achieved. The success will not depend only on the ability of the FASB and IASB to work together, but also on the willingness of national regulators to cooperate and to avoid issuing local interpretation of IFRS. In April 2005, SEC published the road map. This is an article by then Chief Accountant discussed the possible elimination of the US GAAP reconciliation for foreign private issuers that use IFRS. This Road map laid out a series of milestones which if achieved would result in the elimination of the US GAAP reconciliation by 2009, so quite soon. It is often noted that the process of IASC standards are influenced by Anglo-American approach, which partly explains the reserve of certain countries to adopt the international accounting standards. The difference between Anglo-American philosophies and European ones can be explained by the importance attached to two essential characteristics of accountancy: reliability and relevance. To conclude, despite the existence of many convergence points, this research show several major differences between two countries supposed to follow relatively similar rules. This thus tends to catch our attention on the difficulty of international harmonization. This study seems to illustrate perfectly (unfortunately? difficulties of the international accounting harmonization. It could be interesting to carry out a reflection on other ways of making accountancies comparable in order to avoid a fundamental opposition. However, new laws gave (or will give) to companies of several countries, including France and Germany; the possibility of presenting their group accounts according to the international standards, in particular those of the IASC and USGAAP, rather than the national rules. Almost all th e companies having a world activity do it already, or will probably do it soon. BIBLIOGRAPHY †Evolution of research on international accounting harmonization : a historical and insitutional perspective â€Å", Socio-Economic Review, October 2007 Bosco T. , Corporate Accounting Information Systems Cook D. Connor L. , UK/US GAAP Comparison Wolk H. , Dodd J. , Accounting Theory, 7th edition Elliott B. and Elliott Jamie, Financial Accounting and Reporting, 8th edition Ernst Whinney, L’Impact de la septieme directive: la consolidation des comptes en Europe, ETP, 1985 Heem G. t Aonzo P. (2003),  « La normalisation comptable internationale: ses acteurs, sa legitimite,ses enjeux  », Revue d’Economie Financiere IASC, International Accounting Standards Explained, Wiley, 2000 Ortiz E. (2005),  « GAAP choice by European companies  », European Business Review POWER Michael, La Societe de l’audit, La Decouverte, 2005 Price Waterhouse Coopers ; â€Å"IFRS 2005 divergences France /IFRS† ; Editions Francis Lefebvre Street D. L. and Gra y S. J. et Brayant S. M. 1999),  « Acceptance and observance of International Accounting Standards  », The International Journal of Accounting â€Å"Trends in research on international accounting harmonization â€Å", The International Journal of Accounting, September 2007 Weetman P. E. , Jones A. E. , Adams C. A. and Gray S. J,  « Profit measurement and UK accounting standards: a case of increasing disharmony in relation to US GAAP and IAS’s â€Å". Websites: www. wikipedia. fr www. lesechos. fr www. focusifrs. com www. fasb. gov www. investopedia. com www. ey. com www. authorstream. com How to cite International Classification of Accounting Systems, Papers

Present Case That While Violet Is A Partner -Myassignmenthelp.Com

Question: Discuss About The Present Case That While Violet Is A Partner? Answer: Introducation Issue: An analysis of the facts that are present in this question reveals the issue if the law allows Friendly Bank to the loan from Violet and Sonny. That was given to Busy Bee Florist Shop. For this purpose, it needs to be seen if both of them can be treated as the partners of Busy Bee Florist Shop. Rule: The legal provisions that Ireland in the present case include section 1 of the Partnership Act. It has been provided by the Partnership Act that there are three elements that should be present in order to describe the relationship between the parties as a partnership. Hence if the parties are carrying on a business; in common; and for making a profit, the relationship between the parties can be mentioned as a partnership. On the other hand, even if one of these elements is not present, the relationship will not be considered by the law as it was mentioned. For deciding the question if the parties are 'carrying on a business' , it is required to be considered if there is some repetitiveness of action or even if a single action can also be sufficient in this regard. In a number of decisions that have been given by the courts on this issue, it has been stated by the courts that it is necessary that there should be some repetitiveness of action or continuity of action. An example i n this regard can be given of Smith v Anderson, 1880. In this case, a group of depositors had made a decision to purchase the shares of different submarine cable companies. For this purpose, they have formed the trust. The trustees sold his shares these investors and provided them with certificates. Under the circumstances, the court was required to determine if this trust, amounts to a partnership or not. For deciding this issue, the court decided to look at the nature of the business and also the relationship that was present among the parties who were involved in the trust. In particular, the court noted the fact that the trustees have not been provided with the authority to speculate. In the same way, the trustees did not have mutual rights and obligations. In view of all these facts, and keeping in mind the nature of the trust, a conclusion was made by the court that the present case the trust cannot be described as a partnership. The reason behind this decision of the court wa s that there was no association present between the parties that can be described as 'carrying on business'. The Partnership Act also provides the rules that can be used in order to decide if the relationship of the parties can be mentioned as a partnership. However, it is worth mentioning at this point that the decision if a particular relationship can be described as a partner cannot be made only by applying these rules. As a result, these rules alone cannot provide the basis for making the decision regarding a relationship to be termed as a partnership. Hence, the law requires that the court should consider all the circumstances that are present regarding the agreement concluded between the parties. As a result, the court has to find out the real substance of such an agreement (Canny Gabriel Castle Advertising Pty Ltd Anor v Volume Sales (Finance) Pty Ltd., 1974). In the same way, the express, as well as the implied the intention of the parties is also important in this regard. For example, the court has stated in Wiltshire v Kuenzli, 1945 that it was the intention of the parties to do everything which makes them partners and as a result, the intention of going to which the parties should not be treated as partners, was invalid. In the same way, in Stekel v Ellice (1973), the defendant was an employee in an accounting firm belonging to the plaintiff. It was mentioned in the first agreement created between the parties in 1969, that the plaintiff was going to become a salaried partner and he will be given a salary. It was also mentioned that another agreement will be created by the parties. According to the segment, the plaintiff was going to become a full partner. It was also mentioned between the parties that the term of employment was in 1969. Similarly, only the defendant was going to be liable for the losses of the business. The latest agreement was never created by the parties, and they continued to operate in the same way till August, 1970 when the relationship between the parties broke down. The traditional left the business and also sought a declaration acc ording to which the partnership has ended and the court should order the partnership to be wound up. After going through all the facts of the case, the court arrived at the conclusion that the relationship between the parties was a partnership and it continued even if the parties have not entered into an exclusive agreement (Exparte Coral Investments Pty Ltd., 1979). Another relevant provision is also present in the partnership Act. According to section 2(3) of the Act, it has to be treated as a prima facie proof of the fact regarding the presence of a partnership, when a person receives a share of the profit made by the business. However, it also needs to be mentioned that only the fact of sharing the profit made by the business or by receiving payment. That has been generated on the basis of the profit made by the business is not the only effect on the basis of which it can be claimed that such person is a partner in the business (Television Broadcasters Ltd v Ashtons Nominees Pty Ltd., 1979). In this regard, sometimes it difficulty may be present due to the fact that the term 'evidence' has been qualified by using the term 'prima facie'. Therefore, in view of this, it can be concluded that when a profit-sharing scheme is present, it can be considered as evidence suggesting the existence of a partnership, but a person cannot be termed as a part ner only due to the fact that the person shares the profit made by the business. In this regard an important case is of Cox v Hickman (1880). Application: In this case, the Smiths were trading as partners. However, after some time, the company fell prey to financial difficulties. As a result, B. and J. Smith entered into an agreement with their creditors. It was mentioned in this agreement that the business was going to be assigned to the creditors. The creditors will allow the carry on the business under new name. Similarly, the agreement provided that the profit made by the business was going to be divided among all the creditors. According to this agreement, when the creditors have been repaid in full, they will return the business to business to the Smiths. Under these circumstances, two of the creditors were appointed as trustees, Cox and Wheatcroft. However, Cox did not act as the trustee and similarly Wheatcroft also acted in this position for a brief period. After Wheatcroft left his position as the trustee, the other trustees incur some debts, and they also drawn some bills of exchange to Hickman. In such circumstances, Hickma n applied to the court as he wanted that Wheatcroft and Cox should go to the liability for these bills. However, after considering all the facts, the decision of the court was that Wheatcroft and Cox were never mentioned as partners. At the same time, Hickman did not have any knowledge regarding the presence of the deed. Therefore, the court stated that Wheatcroft and Cox cannot be held liable for these debts even if they were sharing the profit. The court relied on the fact that only due to the reason that they were receiving a share from the profit of the business, it cannot be concluded that both of them should be treated as partners. The fact was noted by the court that the arrangement according to which the profit of the business was to be used for repaying the old debts and the creditors agreed to give up their right of the page from the capital of the business, it cannot be said that there was a partnership for the third parties who were not aware of the deed. The Partnership Act also provides that only on the basis of the fact the receiving debt at the liquidited demand from the profit earned by the business. It cannot be claimed that the person has to be treated as a partner. This rule is based on the judgment of the court delivered in Cox v Hickman (1860). On the other hand, when certain circumstances are present, due to which, it becomes clear that in reality the relationship was a partnership, the law provides that the lender can be treated as a partner irrespective of the intention that has been mentioned by the parties. Conclusion: Under these circumstances, in the present case also, by applying the legal rules that are present in the partnership Act, it is clear that Violet can be considered as a partner of Busy Bee Florist Shop. This conclusion can be drawn even if the agreement made between the parties provides that the lender (Violet) is not going to be treated as a partner in the business. However, the same conclusion cannot be made regarding Sonny. As a result, it cannot be concluded that Sonny is also a partner in Busy Bee Florist Shop. This conclusion has been made in the present case on the basis of the fact that according to the law of partnership, it has been mentioned that although the fact that a person receives a share out of the profit of the business but only on the basis of this fact, a conclusion cannot be drawn that the person needs to be treated as a partner (Badeley v Consolidated Bank, 1888). Therefore even if the person may be receiving a share, from the profit of the business or a paymen t that is based on the profit of the business, it cannot be concluded that such person is a partner only due to this fact alone. Hence, the law of partnership provides that the contract for remuneration that is going to be provided to servant or an agent as a share, from the profit of the business does not necessarily mean that such person is a partner and as a result, liable for the debts of the partnership. Therefore it is clear in the present case that while Violet is a partner, Sonny is only a creditor. References Badeley v Consolidated Bank (1888) 38 Ch D 238 Canny Gabriel Castle Advertising Pty Ltd Anor v Volume Sales (Finance) Pty Ltd (1974) 131 CLR 321 Cox v Hickman (1880) 8 HL Cas 268 Exparte Coral Investments Pty Ltd [1979] Qd R 292 Re Ruddock (1879) 5 VLR 51 (IP M) 51 Smith v Anderson (1880) 15 Ch D 247 Stekel v Ellice [1973] 1 WLR 191 Television Broadcasters Ltd v Ashtons Nominees Pty Ltd (No 1) (1979) 22 SASR 552 Wiltshire v Kuenzli (1945) 63 WN 47