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UNITED NATIONS WORK

Posted by Unknown Saturday, 1 February 2014 0 comments

UNITED NATIONS WORK


  • Provides food to 90 million peoples in 75 countries 
  • Vaccinates 58 per cent of the world's children, saving 2.5 million lives a year
  • Assists over 34 million refugees and people fleeing war, famine or persecution
  • Combats climate change, works with 140 nations to prevent harmful mercury emissions
  • Keeps peace with 120,000 peacekeepers in 16 operations on 4 continents
  • Fights povetry, helping 370 million rural poor achieve better lives in the last 30 years 
  • Protects and promotes human rights on site and through some 80 treaties/diclarations
  • Mobilizes US$12.5 million in humanitarian aid to help people affected by emergencies 
  • Uses diplomacy to prevent conflict; assist some 50 countries a year with elections
  • Promotes maternal health, saving the lives of 30 million women a year


*source-UNITED NATIONS-Department of Public Information-2013

WORLD TOURISM DAY

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WORLD TOURISM DAY


World Tourism Day(WTD) is held annually on 27 september. Its purpose is to foster awareness among the international community of the importance of tourism and its social, cultural, political and economic value. WTD is celebrated by events around the themes selected by the UNWTD General Assembly, on the recommendation of the UNWTO Executive council.

In Line with the 2013 United Nations International Year of Water co-operation, the 2013 theme for World Tourism Day was Tourism and Waters Protecting over common future.

Arms Trade Treaty (ATT)

Posted by Unknown Sunday, 26 January 2014 0 comments
The Arms Trade Treaty (ATT) is a multilateral treaty that regulates the international trade in conventional weapons, which has not entered into force. International weapons commerce has been estimated to reach US$70 billion a year.
It must be workable and enforceable. It must:
  • provide guidelines for the treaty's full, clear implementation;
  • ensure transparency—including full annual reports of national arms transfers;
  • have an effective mechanism to monitor compliance;
  • ensure accountability—with provisions for adjudication, dispute settlement and sanctions;
  • include a comprehensive framework for international cooperation and assistance.

Provisions of the Arms Trade Treaty (ATT) =
  • be used in serious violations of international human rights or humanitarian law, or acts of genocide or crimes against humanity;
  • facilitate terrorist attacks, a pattern of gender-based violence, violent crime or organized crime;
  • violate United Nations Charter obligations, including UN arms embargoes;
  • be diverted from its stated recipient;
  • adversely affect regional security; or
  • seriously impair poverty reduction or socioeconomic development.

GLOBAL NUTRITION FOR GROWTH PACT

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World leader signed a global agreement to fight malnutrition in children and made commitments of up to 4.15 billion dollars to tackle under nutrition up to 2020. The agreement, called Global Nutrition for Growth was signed during central London summit.


The participants who signed a Global Nutrition for Growth Compact- Committed  their countries and organizations by 2020 to :


  • Improving the nutrition of 500 million pregnant women and young children
  • Reducing the number of children under five who are stunted by an additional 20 million
  • Saving the lives of at least 1.7 million children by preventing stunting, increasing breastfeeding and better treatment of severe and acute malnutrition.

CROATIA, 28TH MEMBER OF EU

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Croatia has become the 28th member of the European Union. Croatia is the first country to join the EU since 2007, when bulgaria and Romania came on board, and only the second of the seven ex-Yugoslav states after Slovenia which part of the big bang eastward enlargement in 2004. The path to join has been more exacting, with EU having learnt that once countries join the bloc they lose momentum to reform , and particularly, to tackle corruption. It had applied for EU membership in 2003. 

Carbon Emission Trade

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An exchange of credits between nations designed to reduce emissions of carbon dioxide. The carbon trade allows countries that have higher carbon emissions to purchase the right to release more carbon dioxide into the atmosphere from countries that have lower carbon emissions. The carbon trade originated with the 1997 Kyoto Protocol and is intended to reduce overall carbon dioxide emissions to 5% below 1990 levels between 2008 and 2012.
CHINA IS THE LARGEST CARBON GAS EMITER IN THE WORLD.

SYRIA JOINS OPCW CONVENTION

Posted by Unknown Friday, 24 January 2014 0 comments
    Syria officially joined the Organization for the Prohibition of Chemical Weapons(OPCW), United Nations convention banning chemical weapons. This made the country the 190th state party to the OPCW. Only six states have yet to sign the international treaty.

Statistics from OPCW=

190 nations, 98% of the global population, have joined the OPCW.
58,172, or 81.71%, of the world's declared stockpile of 71,196 metric tonnes of chemical agent have been destroyed.
5,286 inspections have taken place at 228 chemical weapon-related and 1,905 industrial sites on the territory of 86 States Parties since April 1997. Worldwide, 4,913 industrial facilities are liable to inspection.

Asian Development Bank (ADB)

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The Asian Development Bank (ADB) is a regional development bank established on 22 August 1966 to facilitate economic development of countries in Asia. The bank admits the members of the United Nations Economic and Social Commission for Asia and the Pacific and non-regional developed countries. From 31 members at its establishment, ADB now has 67 members - of which 48 are from within Asia and the Pacific and 19 outside. ADB was modeled closely on the World Bank, and has a similar weighted voting system where votes are distributed in proportion with member's capital subscriptions.

United Nations Framework Convention on Climate Change

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The United Nations Framework Convention on Climate Change (UNFCCC or FCCC) is an international environmental treaty negotiated at the United Nations Conference on Environment and Development (UNCED), informally known as the Earth Summit, held in Rio de Janeiro from 3 to 14 June 1992. The objective of the treaty is to "stabilize greenhouse gas concentrations in the atmosphere at a level that would prevent dangerousanthropogenic interference with the climate system".
The treaty itself set no binding limits on greenhouse gas emissions for individual countries and contains no enforcement mechanisms. In that sense, the treaty is considered legally non-binding. Instead, the treaty provides a framework for negotiating specific international treaties (called "protocols") that may set binding limits on greenhouse gases.
The UNFCCC was opened for signature on 9 May 1992, after an Intergovernmental Negotiating Committee produced the text of the Framework Convention as a report following its meeting in New York from 30 April to 9 May 1992. It entered into force on 21 March 1994. As of May 2011, UNFCCC has 195 parties.

Green Climate Fund(GCF)

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The purpose of the Green Climate Fund is to make a significant and ambitious contribution to the global efforts towards attaining the goals set by the international community to combat climate change.

The Fund will contribute to the achievement of the ultimate objective of the United Nations Framework Convention on Climate Change (UNFCCC). In the context of sustainable development, the Fund will promote the paradigm shift towards low-emission and climate-resilient development pathways by providing support to developing countries to limit or reduce their greenhouse gas emissions and to adapt to the impacts of climate change, taking into account the needs of those developing countries particularly vulnerable to the adverse effects of climate change.

Russia Successfully Launched Proton-M Rocket

Posted by Unknown Friday, 17 January 2014 0 comments


Russia Successfully Launched Proton-M


 Russia on 12 November 2013 successfully launched the Proton-M rocket carrying a defense satellite, Raduga-1M from its Baikonur cosmodrome in Kazakhstan. 

It is important to note that Russia restarted the launch of Proton rockets in September 2013 after a small gap in order to check why a Proton rocket launched on 2 July 2013 exploded while taking off. The Proton-M rocket is the most popular rocket of Russia for the commercial satellite launches. 

 About the Raduga-1M Defense Satellite

• Raduga-1M is primarily a defense satellite of the third generation.
• It is a part of the Stage Two Unified Satellite Telecommunications System.
• It is equipped with the multichannel transponder equipment, which enables it to establish reliable communications with mobile geo-service stations. 

What is a Proton-M rocket?

Proton-M rocket is a Russian carrier rocket which is derived from Soviet-developed Proton. Proton is actually an expendable launch system which is used for commercial as well as Russian Government space launches. 

Proton-M rocket is built by Khrunichev and launched from sites 81 and 200 at the Baikonur Cosmodrome in Kazakhstan. The commercial launches of Proton-M rocket are marketed by International Launch Services (ILS). First Proton-M launch took place on 7 April 2001. 

All the Protons are built at the Khrunichev plant in Moscow. These are then transported for the launch to Baikonur Cosmodrome from where they are raised into the vertical position for the purpose of launch.

 The Proton-M, GRAU index 8K82M or 8K82KM, is a Russian carrier rocket derived from the Soviet-developed Proton. It is built byKhrunichev, and launched from sites 81 and 200 at the Baikonur Cosmodrome in Kazakhstan. Commercial launches are marketed by International Launch Services (ILS), and generally use Site 200/39. The first Proton-M launch occurred on 7 April 2001.

World Bank

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World Bank


The World Bank is an international financial institution that provides loans[3] to developing countries for capital programs. The World Bank's official goal is the reduction of poverty.


  1. Eradicate Extreme Poverty and Hunger: From 1990 through 2004, the proportion of people living in extreme poverty fell from almost a third to less than a fifth. Although results vary widely within regions and countries, the trend indicates that the world as a whole can meet the goal of halving the percentage of people living in poverty. Africa's poverty, however, is expected to rise, and most of the 36 countries where 90% of the world's undernourished children live are in Africa. Less than a quarter of countries are on track for achieving the goal of halving under-nutrition.
  2. Achieve Universal Primary Education: The percentage of children in school in developing countries increased from 80% in 1991 to 88% in 2005. Still, about 72 million children of primary school age, 57% of them girls, were not being educated as of 2005.
  3. Promote Gender Equality: The tide is turning slowly for women in the labor market, yet far more women than men- worldwide more than 60% – are contributing but unpaid family workers. The World Bank Group Gender Action Plan was created to advance women's economic empowerment and promote shared growth.
  4. Reduce Child Mortality: There is some what improvement in survival rates globally; accelerated improvements are needed most urgently in South Asia and Sub-Saharan Africa. An estimated 10 million-plus children under five died in 2005; most of their deaths were from preventable causes.
  5. Improve Maternal Health: Almost all of the half million women who die during pregnancy or childbirth every year live in Sub-Saharan Africa and Asia. There are numerous causes of maternal death that require a variety of health care interventions to be made widely accessible.
  6. Combat HIV/AIDS, Malaria, and Other Diseases: Annual numbers of new HIV infections and AIDS deaths have fallen, but the number of people living with HIV continues to grow. In the eight worst-hit southern African countries, prevalence is above 15 percent. Treatment has increased globally, but still meets only 30 percent of needs (with wide variations across countries). AIDS remains the leading cause of death in Sub-Saharan Africa (1.6 million deaths in 2007). There are 300 to 500 million cases of malaria each year, leading to more than 1 million deaths. Nearly all the cases and more than 95 percent of the deaths occur in Sub-Saharan Africa.
  7. Ensure Environmental Sustainability: Deforestation remains a critical problem, particularly in regions of biological diversity, which continues to decline. Greenhouse gas emissions are increasing faster than energy technology advancement.
  8. Develop a Global Partnership for Development: Donor countries have renewed their commitment. Donors have to fulfill their pledges to match the current rate of core program development. Emphasis is being placed on the Bank Group's collaboration with multilateral and local partners to quicken progress toward the MDGs' realization.

Luther Gulick and Lyndall Urwick(Administrative Thinker)

Posted by Unknown Tuesday, 8 October 2013 0 comments

Luther Gulick and Lyndall Urwick


In Brief

The contribution of Gulick and Urwick to the administrative theory are summarized below :
  • Luther Gulick, an acknowledged founder of administrative thought, and Lyndall Urwick, an outstanding management consultant with their rich experience in civil and military administration made contribution to the synthesis of classical administrative theory.
  • The papers on the Science of Administration, edited by them, is considered a landmark in the development of the science of administration. In their view the process of development in engineering science, which is based on empirical observations and analysis, is equally applicable to the development of science of administration.
  • Gulick and Urwick emphasised the importanceof structure in administration. They considered structure as a designing process and devoted their attention to the discovery of principles based on which the structure may be designed. They considered principles as a framework of thought and arrangements of ideas to help in the development of science of administration.
  • Gulick discussed in detail the executive functions and coined POSDCORB By incorporating the first letters of all the functions of the executive. The acronym, though not comphrensive, helps in understanding and analysing the functions of the executive.
  • Gulick considered division of work as the basis of organization. His theory of departmentalization addresses the basis of division of work for the creation of departments. The four basis of departmentalization viz., purpose, process, persons and place, popularly known as the "4Ps", are extensively used in the creation of departments/units in organizations. Gulick and Urwick in their writings in detail the application of many other principles like single executive, staff principles, delegation, span of control, etc.
  • Gulick, in his later writings focused on human factors in administration. Based on his fifty years of analysis, Gulick observes:"after all governments are constituted of human beings, are run by human beings and have as their main job, helping, contributing and serving human beings". He considered the human being as the dynamic factor intrinsic in the study of administration.
  • Gulick also emphasised time as the crucial factor in the organizations. He identified five aspects of time, viz., time as input, time as an output, time as the flow of events and time as a gap between two or more significant events or processes and finally timing as a management policy. He consisders time factor as critical in public administration.
  • The principles of organization of Gulick and Urwick were criticised for their contradictions and inadequacy to answer practical organizational questions and also for their neglect of role of human element in organizational processes. In his later writings Gulick emphasised the role of human beings in organizations; and 
  • There can not be any serious of the science of administration without reference to the principles of organization. Understanding and theorising the dynamic nature of application of these principles in different administrative situations is the major challenge of administrative studies today.


MAX WEBER(Administrative Thinkers)

Posted by Unknown Monday, 7 October 2013 0 comments
MAX WEBER



In brief
Weber’s contribution to the study of bureaucracy can be summarized as :

·                Max Weber, a broad-based scholar with academic interest spanning economic, history, politics, religion and society made a significant contribution to the analysis and  understanding of bureaucracy. Today, there cannot be any study or discussion on bureaucracy without reference to Max Weber.
·           
           Weber defined administration as exercise as authority and identified different forms of legitimacy viz., traditional, charismatic and legal and analyzed the nature of exercise of authority in ideal-type authority.

·                Weber considered legal authority as rational and called it legal-rational. He considered bureaucracy, the institutional form of legal-rational authority, as the most appropriate to modern governments.

·              He described in detail the characteristics of legal ration bureaucracy which is popularly known as Weberian Model of  bureaucracy.

·             Weber laid stress on legitimacy of legal-rational authority which is based on impersonal orders, rules, sphere of competence, hierarchy, written documents, technically qualified people and separation of personal and public ends.

·             Weberian model of bureaucracy attracted criticism mainly on three grounds i.e. rationality, suitability of model to different places and changing times, and its ability to attain maximum efficiency.

·              The core of criticism is on its emphasis on structure and neglect of human behavior. The model is described by some as a structural approach to organizations.

·                The webwrian model has both positive and negative features. In assessing Weberian ideal type, the historical context of Germany of his time should be kept in mind.


·               The Weberian model continues to be the framework for the analysis, criticism and for improvements in bureaucracy. That is the immortality of the model. 



FREDERICK TAYLOR(Administrative Thinker)

Posted by Unknown Friday, 4 October 2013 0 comments

FREDERICK TAYLOR



In Brief,

Frederick Taylor's contribution to a management and administration can be summarized as :

  • Frederick Winslow Taylor, a mechanical engineer by training, was regarded as the "Father of Scientific Management" for pioneering work in the study of human being at work;
  • Based on extensive studies of industrial work situation, Taylor identified defects in management and proposed a philosophy of management  for industrial efficiency, which was subsequently labelled as "Scientific Management" by Louis Brandies;
  • Taylor's Philosophy of scientific management is that there is no inherent conflict in the interests of employee, workers and consumers. Based on this philosophy he developed four principles of scientific management viz., a) development of true science of work; b) scientific selection of work; c) scientific education and development of workers; and d) intimate and friendly cooperation between the management and the men;
  • Taylor developed many management techniques like functional foremanship; time and motion study; piece-rate system; standardization of tools; the exception principles; the differential rate system, etc., as application tools of scientific management. The tools, Taylor felt, will help in identifying "one best way of doing things";
  • The essence of scientific management, according to Taylor, is mental revoloution i.e. change of attitude on the part of workers and management towords their work and their relationships;
  • Both trade unions and managers of the day were very critical of scientific management, through for different reasons. The trade union consisdered the scientific management as anti-labour and anti-trade union, focusing on mechanical aspects of work ignoring the human aspects. The labour organizations protested the "dehumanising" aspect of Taylorism;
  • The manager did not appreciate the criticism of rule-of-thumb methds and prescription of technical training to managers to increase efficiency and effectiveness in organizations;
  • Taylor's principles and prescriptions were criticised by latter writers for their failure to understand the anatomy of work. Simon and March characterized scientific management as the "psychological organization theory";
  • Taylor's work, in spite of limitationsand criticisms, greatly influenced the study and practices of industrial administration in the modern world. Taylor's heritage is visible in many modern management techniques like operation research, method study, Time study, etc. Taylor should be given due credit for laying foundation for the systematic study of work and worker.  

Henry Feyol(Administrative Thinker)

Posted by Unknown Wednesday, 2 October 2013 0 comments

Henry Feyol




Henri Fayol's contribution to the theory of oublic administration is as follows :

  • Henri Fayol, a successful executive of a mining of company in France, made significant contribution to the management concepts and is considered as the founder of "Management Process School".
  • He considered management as a science which can be developed, studied and applied equally well to public and private affairs.
  • He emphasised the university of management processes and made a distinction between management and public administration.
  • He identified five elements of organization viz., planning, organization, command, coordination and control.
  • Fayol derived fourteen principles of administration which are capable of adoption to various enterprises and settings. He emphasised the importance of training in administration.
  • Although Fayol places great emphasis on formal organization, he is alive to the limitations of the hierarchy and formalism. Therefore, he suggested Gangplank - "level jumping" - in hierarchical organization.
  • A comparison of contributors of Henri Fayol, a French Manager and F.W.Taylor, an American engineer is useful to understand the complementarity of their contributions and the differences in their approach and focus. Taylor focused mainly on the management principles to be directly applied to the field of production and Fayol mainly focused on the development of general theory of administration to be applied at the top management level.
  • Fayol's theory of functionalism is criticised for its narrow focus, mechanical approach and neglect of complex factors affecting human behaviour in organizations.
  • Fayol's framework of systematic analysis of administrative process stimulated subsequent writers on administration and management. His principles of administration, in variant form, are applied in the working of modern organizations.

Woodrow Wilson (Administrative Thinker)

Posted by Unknown Thursday, 19 September 2013 0 comments
Woodrow Wilson




Woodrow Wilson’s contribution to the field of public administration may be summarized as :


§  Wilson laid the intellectual roots for the emergence of public administration as a field/subject of enquiry through his essay “ The Study of Administration” in 1887.
§  “ The Study of Administration” traced the history of administration as a new development political science, presented the value of the study and indicated the methods by means which it ought to be carried.
§  “ The Study of Administration” was the result of Wilson’s search to find answers to the political abuses of the spoil system and finding ways of assimilation of European administrative systems into  American democratic politics.
§  He emphasized  the importance study of administration in the context of increasing complexity in society, increasing role of state and democratic nature of governments.
§  Wilson considered administration eminently a science and pleaded for the development of clear concepts of good administration.
§  He examined the relationship between politics and administration and considered them as separate activities at one level and interdependent at another. This vagueness lead to different interpretations of his views on politics and administration relationships.
§  He focused on the implementation aspects of the government and advocated the need for technically competent civil service based on merit.
§  Wilson emphasized the importance of comparative method, particularly learning from others about the ways of doing things without learning without learning their motives and ends; and

§  “ The Study of Administration” was too general, too broad and too vogue, as Wilson himself put it. It gave scope for different interpretations of Wilson’s views and also assessment of his contribution to the study of public administration. Looking in a historical context when the political debate was mainly on “who” should make laws and “what” the laws should be, his focus on “how” law should be ‘administered’ is a seminal contribution.



Profit and Loss Formulae

Posted by Unknown Sunday, 8 September 2013 0 comments

Profit and Loss Formulae 



Probability – Sample space for two dice (outcomes)

Posted by Unknown Wednesday, 4 September 2013 0 comments
Probability – Sample space for two dice (outcomes):
Probability for Rolling Two Dice
Note:
(i) The outcomes (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6) are called doublets.
(ii) The pair (1, 2) and (2, 1) are different outcomes.

Worked-out problems involving probability for rolling two dice:
1. Two dice are rolled. Let A, B, C be the events of getting a sum of 2, a sum of 3 and a sum of 4 respectively. Then, show that
(i) A is a simple event
(ii) B and C are compound events
(iii) A and B are mutually exclusive
Solution: 
Clearly, we have
A = {(1, 1)}, B = {(1, 2), (2, 1)} and C = {(1, 3), (3, 1), (2, 2)}.
(i) Since A consists of a single sample point, it is a simple event.
(ii) Since both B and C contain more than one sample point, each one of them is a compound event.
(iii) Since A ∩ B = ∅, A and B are mutually exclusive.
2. Two dice are rolled. A is the event that the sum of the numbers shown on the two dice is 5, and B is the event that at least one of the dice shows up a 3.
Are the two events (i) mutually exclusive, (ii) exhaustive? Give arguments in support of your answer.
Solution: 
When two dice are rolled, we have n(S) = (6 × 6) = 36.
Now, A = {(1, 4), (2, 3), (4, 1), (3, 2)}, and
B = {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (1,3), (2, 3), (4, 3), (5, 3), (6, 3)}
(i) A ∩ B = {(2, 3), (3, 2)} ≠ ∅.
Hence, A and B are not mutually exclusive.
(ii) Also, A ∪ B ≠ S.
Therefore, A and B are not exhaustive events.

More examples related to the questions on the probabilities for throwing two dice.
3. Two dice are thrown simultaneously. Find the probability of:
(i) getting six as a product
(ii) getting sum ≤ 3
(iii) getting sum ≤ 10
(iv) getting a doublet
(v) getting a sum of 8
(vi) getting sum divisible by 5
(vii) getting sum of atleast 11
(viii) getting a multiple of 3 as the sum
(ix) getting a total of atleast 10
(x) getting an even number as the sum
(xi) getting a prime number as the sum
(xii) getting a doublet of even numbers
(xiii) getting a multiple of 2 on one die and a multiple of 3 on the other die
Solution: 
Two different dice are thrown simultaneously being number 1, 2, 3, 4, 5 and 6 on their faces. We know that in a single thrown of two different dice, the total number of possible outcomes is (6 × 6) = 36.
(i) getting six as a product:
Let E1 = event of getting six as a product. The number whose product is six will be E1= [(1, 6), (2, 3), (3, 2), (6, 1)] = 4
Therefore, probability of getting ‘six as a product’
               Number of favorable outcomes
P(E1) =     Total number of possible outcome 

      = 4/36
      = 1/9

(ii) getting sum ≤ 3:
Let E2 = event of getting sum ≤ 3. The number whose sum ≤ 3 will be E2 = [(1, 1), (1, 2), (2, 1)] = 3
Therefore, probability of getting ‘sum ≤ 3’
               Number of favorable outcomes
P(E2) =     Total number of possible outcome 

      = 3/36
      = 1/12

(iii) getting sum ≤ 10:
Let E3 = event of getting sum ≤ 10. The number whose sum ≤ 10 will be E3 =
[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),
(6, 1), (6, 2), (6, 3), (6, 4)] = 33
Therefore, probability of getting ‘sum ≤ 10’
               Number of favorable outcomes
P(E3) =     Total number of possible outcome 

      = 33/36
      = 11/12

(iv) getting a doublet: Let E4 = event of getting a doublet. The number which doublet will be E4 = [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)] = 6
Therefore, probability of getting ‘a doublet’
               Number of favorable outcomes
P(E4) =     Total number of possible outcome 

      = 6/36
      = 1/6

(v) getting a sum of 8:
Let E5 = event of getting a sum of 8. The number which is a sum of 8 will be E5 = [(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)] = 5
Therefore, probability of getting ‘a sum of 8’
               Number of favorable outcomes
P(E5) =     Total number of possible outcome 

      = 5/36

(vi) getting sum divisible by 5:
Let E6 = event of getting sum divisible by 5. The number whose sum divisible by 5 will be E6 = [(1, 4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), (6, 4)] = 7
Therefore, probability of getting ‘sum divisible by 5’
               Number of favorable outcomes
P(E6) =     Total number of possible outcome 

      = 7/36

(vii) getting sum of atleast 11:
Let E7 = event of getting sum of atleast 11. The events of the sum of atleast 11 will be E7 = [(5, 6), (6, 5), (6, 6)] = 3
Therefore, probability of getting ‘sum of atleast 11’
               Number of favorable outcomes
P(E7) =     Total number of possible outcome 

      = 3/36
      = 1/12

(viii) getting a multiple of 3 as the sum:
Let E8 = event of getting a multiple of 3 as the sum. The events of a multiple of 3 as the sum will be E8 = [(1, 2), (1, 5), (2, 1), (2, 4), (3, 3), (3, 6), (4, 2), (4, 5), (5, 1), (5, 4), (6, 3) (6, 6)] = 12
Therefore, probability of getting ‘a multiple of 3 as the sum’
               Number of favorable outcomes
P(E8) =     Total number of possible outcome 

      = 12/36
      = 1/3

(ix) getting a total of atleast 10:
Let E9 = event of getting a total of atleast 10. The events of a total of atleast 10 will be E9 = [(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)] = 6
Therefore, probability of getting ‘a total of atleast 10’
               Number of favorable outcomes
P(E9) =     Total number of possible outcome 

      = 6/36
      = 1/6

(x) getting an even number as the sum:
Let E10 = event of getting an even number as the sum. The events of an even number as the sum will be E10 = [(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 3), (3, 1), (3, 5), (4, 4), (4, 2), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)] = 18
Therefore, probability of getting ‘an even number as the sum
               Number of favorable outcomes
P(E10) =     Total number of possible outcome 

      = 18/36
      = 1/2

(xi) getting a prime number as the sum:
Let E11 = event of getting a prime number as the sum. The events of a prime number as the sum will be E11 = [(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)] = 15
Therefore, probability of getting ‘a prime number as the sum’
               Number of favorable outcomes
P(E11) =     Total number of possible outcome 

      = 15/36
      = 5/12

(xii) getting a doublet of even numbers:
Let E12 = event of getting a doublet of even numbers. The events of a doublet of even numbers will be E12 = [(2, 2), (4, 4), (6, 6)] = 3
Therefore, probability of getting ‘a doublet of even numbers’
               Number of favorable outcomes
P(E12) =     Total number of possible outcome 

      = 3/36
      = 1/12


(xiii) getting a multiple of 2 on one die and a multiple of 3 on the other die:
Let E13 = event of getting a multiple of 2 on one die and a multiple of 3 on the other die. The events of a multiple of 2 on one die and a multiple of 3 on the other die will be E13 = [(2, 3), (2, 6), (3, 2), (3, 4), (3, 6), (4, 3), (4, 6), (6, 2), (6, 3), (6, 4), (6, 6)] = 11
Therefore, probability of getting ‘a multiple of 2 on one die and a multiple of 3 on the other die’
               Number of favorable outcomes
P(E13) =     Total number of possible outcome 

      = 11/36


4. Two dice are thrown. Find (i) the odds in favour of getting the sum 5, and (ii) the odds against getting the sum 6.
Solution:
We know that in a single thrown of two die, the total number of possible outcomes is (6 × 6) = 36.
Let S be the sample space. Then, n(S) = 36.
(i) the odds in favour of getting the sum 5:
Let E1 be the event of getting the sum 5. Then,
E1 = {(1, 4), (2, 3), (3, 2), (4, 1)} 
⇒ P(E1) = 4
Therefore, P(E1) = n(E1)/n(S) = 4/36 = 1/9
⇒ odds in favour of E1 = P(E1)/[1 – P(E1)] = (1/9)/(1 – 1/9) = 1/8.

(ii) the odds against getting the sum 6:
Let E2 be the event of getting the sum 6. Then,
E2 = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)} 
⇒ P(E2) = 5
Therefore, P(E2) = n(E2)/n(S) = 5/36 
⇒ odds against E2 = [1 – P(E2)]/P(E2) = (1 – 5/36)/(5/36) = 31/5.

These examples will help us to solve different types of problems based on probability for rolling two dice.

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