Probability Theory In Decision Making

Assignment No. 2

QUANTITATIVE TECHNIQUES (5564) Executive MBA/MPA (Col)

RELEVANCY OF PROBABILITY THEORY IN DECISION MAKING

ZAHID NAZIR Roll.No. AB523655 Semester:Autumn 2008 Zahid Nazir – 1st Semester (MBA Col)

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INTRODUCTION TO TOPIC THE MEANING OF PROBABILITY Most of the managerial decisions are decisions related to uncertainty. Tomorrow is not well defined. Managers are required to make some appropriate assumptions for the ‘would be tomorrow’ and base their decisions on such assumptions. The notion of uncertainty or chance is so common in everybody’s life that it becomes difficult to define it. We talk about chances of one’s winning the election, chances of one’s getting a handsome job and a beautiful wife. Infact almost everything happening in our day to day life is a matter of chance. Some people would prefer to call it “Luck” others would say that under uncertainty man is forced to gamble. i.e. under uncertainty decision maker is forced to take risk. Statistically speaking, we attach probability with the occurrence or non occurrence of an event.

RELEVANCE OF PROBABILITY THEORY IN DECISION MAKING Let us have a look at some of the business situations characterized by uncertainty. i).

INVESTMENT PROBLEM A business man having a choice of investing in two different projects, each having different initial investment. The decision has to be taken on the choice, the outcome of which is contingent upon the level of demand.

ii).

INTRODUCING A NEW PRODUCT When a new product is developed, the problem is to decide whether or not to introduce the product in addition to the existing product-mix. The decision maker may not be sure about the acceptability of the product. He conducts a test marketing in three regions and gets contradictory results. Should he drop the idea of introducing a new product? It is necessary to answer the question: What is the probability that the new product introduced will be successful?

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iii).

STOCKING DECISIONS A dealer of a perishable commodity does not know the demand in advance. The commodity gets spoiled if it is not sold by end of the day. He is not sure about the demand pattern, yet he must decide in advance how many units to stock.

iv).

THE INDIVIDUAL INVESTOR An investor who is engaged in buying and selling of equities is trying to optimize his return. The price behavior of securities is subjected to uncertainties, which in turn depend upon numerous factors. In the situations discussed above, managers take decisions on the basis of their forecast of the probable future. They use their “intuition” which may or may not be based on their past experience. The ability to make better decisions, not necessarily optimal, is sometimes referred to as ‘ business acumen’. While working on the basis of intuition, the mangers and businessmen, in fact, have at the back of their mind the concept of probability.

The uncertainty situations can be classified into two categories, first, those situations where an experiment can be conducted repeatedly; secondly, those situations where it is not possible to conduct the experiment either because the cost is prohibitive or because it is physically impossible to conduct the experiment. Managers base their decisions either on the basis of their past experience (the repeated experiment) or on the basis of informed guess, a better term for which will be the subjective probability. DEFINITION OF PROBABILITY The word probability refers to the chances of happening of an event. Thus when we say that chances of winning an election are seventy per cent, we are in fact saying that the probability of winning is 0.7. Let us now define the probability in a Zahid Nazir – 1st Semester (MBA Col)

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more rigorous way. We will define it under two approaches - the Classical Approach and the Bayesian Approach. THE CLASSICAL APPROACH i) Equally Likely: Under the classical approach, it is assumed that each outcome of an experiment is “equally likely”, hence equal probability is assigned to each outcome. Thus if there are only two outcomes in a random experiment, then the probability of each outcome will be 0.5. For example, in tossing a coin, there are only two outcomes i.e. the head up or tail up. Therefore in a single toss of a fair coin, the probability of getting a head up is the same as the probability of getting a tail up and is equal to 0.5. If we roll a six sided die, there are six possible outcomes corresponding to the six sides of the die and each outcome is equally likely. Thus the probability that the face with dots ‘i’ turns up will be P(i)= 1/6 for all values of i, 1,2,3,4,5,6. So far we have discussed the concept of probability of an outcome (simple event). We can use this concept to define the probability of an event, where by an event we mean a combination of simple events. Thus, the probability of an event A is equal to the number of possible outcomes favorable to A divided by the total number of possible outcomes of the experiment, assuming all the outcomes as equally likely. For example, in a throw of a single die, the event “odd number” can occur in three (favorable) ways i.e. 1,3 and 5 of the total six possible equally likely outcomes. Hence the probability of getting an odd number is 3/6 or 0.5. Consider the following numerical examples: a). Find the probability of drawing “a dice” in a single draw from a well shuffled deck of cards. In a deck of 52 cards, i.e. 52 possible outcomes, of which 13 are dice, the probability of drawing a dice is Zahid Nazir – 1st Semester (MBA Col)

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P (Dice)

=

Number of dice cards / Total number of cards

=

13/52 = 0.25

b). In a production run of 500 items, 15 items are found to be defective. If one item is drawn from the production run at random, what is the probability that it will be found defective ? P (Defective)= Number of defective items / Total number of items = ii).

15/500

= 0.03

Relative Frequency Approach ( Empirical Definition): Let us assume that an experiment can be repeated a large number of times under the same conditions and each trial has no influence on subsequent repetitions, i.e. Trials are independent of one another. If the total number of trials is ‘n’ and ‘m’ denotes the number of times the outcome ‘A’ occurs, then the probability of obtaining the event ‘A’ is defined as P (A) =

Limn-x m/n

= p

Thus the probability of ‘A’ is a unique number ‘p’ to which the outcome ultimately settles down. The fraction m/n of the outcome is referred to as the “relative frequency” of the event in ‘n’ trials. If 1000 tosses of a coin result in 519 heads, the probability of head is =

519/1000 = 0.519

If another 1000 tosses result in 491 heads, the probability of head is =

519 + 491/2000 = 0.505

If another 1000 tosses results in 496 heads, then the probability of head is =

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519 + 491 + 496 / 3000 = 0.502

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and so on. Thus the limit is tending to 0.5 and therefore the probability of getting a head is 0.5. Since the ‘m’ cannot take a negative value, and the extreme values it can take is ‘0’ and ‘n’, the probability must lie between 0 and 1 i.e. 0 ≤ p ≤ 1. Thus, the probability of an event is a number between 0 and 1. If the event cannot occur, its probability is 0 and if its occurrence is certain its probability is 1. BAYESIAN APPROACH (Subjective Probability) Managers quite often face problems that have never occurred in the past and will never occur in the future in precisely the same form. Under such circumstances, if the decision maker is making an attempt to quantify the possibility of happening of an event, he is expressing his opinion on the basis of his feelings about the situation and his “degree of rational belief”. Such quantification in terms of a number between 0 and 1 is often referred to as personal or subjective probability. Different decision makers may view the same situation differently, as per their own degree of beliefs, conviction, experience and background, and thus they may assign different probabilities. However the decision maker’s final action will depend upon his own assessment and judgment of the situation. The subjective probability provides a quantitative way to express one’s beliefs and conviction about each outcome. Choosing a number ‘0’ means the decision maker believes that the event is impossible to occur and choosing a number ‘1’ means that he believes that the event is ‘dead sure’ to happen. Any other number between 0 and 1 indicates the decisions maker’s judgment as to the likelihood of occurrence. A complete set of all such numbers for each possible outcome will represent the subjective probability assessment distribution of the way the uncertainty enters the situation under consideration. Zahid Nazir – 1st Semester (MBA Col)

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So, in the real situation, one may assess the probability of happening of an event using one of the above mentioned approaches or a combination of approaches depending upon the availability of historical data and decision maker’s personal judgment.

Approach

Context

Classical Approach

The pattern of outcomes is countable. Experiments can be repeated a large number of times.

Bayesian Approach

Experiments can be performed only once and can not be repeated.

SAMPLE SPACE AND EVENTS In order to understand the concept of probability more clearly, it is necessary to understand certain terms very precisely and the most important is randomness or random experiment. A random experiment can be defined as an experiment having the property that i).

All possible outcomes can be specified in advances.

ii).

It can be repeated any number of times.

iii).

The outcome does not necessarily be the same on different trials so that the actual outcome of the experiment is not known in advance. The number of possible outcomes is either finite or infinite.

The simplest illustration of a random experiment is tossing a coin or a die. Another example is the sex of the first two children born. The term experiment or trial is used to refer to any type of situation that can be Zahid Nazir – 1st Semester (MBA Col)

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experienced on a repeated basis. The basic feature of random experiment is, the outcome is not predictable in advance. This means that there is an uncertainty in the outcome of an experiment. However through the use of probability, something can be said about the frequency of the occurrence in a large number of repeated experiments or trials. To develop the concepts of probability, it is necessary to understand the following terms. A collection of all possible distinct outcomes of an experiment is called the sample space of outcomes. This is also called a set of outcomes. Each distinct outcome of an experiment is called a simple event, an elementary outcome or an element of the sample space. An event is said to occur if the outcome of a random experiment, once performed, is contained within a given event. A sample space is presented either by listing all possible outcomes of an experiment or trial by using convenient symbols to identify the outcomes, or by making a descriptive statement characterizing the set of possible outcomes. Consider the simple example of tossing an unbiased coin twice. The sample space can be represented as follows: { HH, HT, TH, TT } Each possible distinct outcome, such as HH, HT, TH, or TT is considered as an event of this experiment. HH indicates that two heads obtained in a row, HT indicates a head in the first toss and a tail in the second and so on. In studying the performance of industries, one can define the sample space as follows: all industries declaring the dividends during the last two consecutive financial years Zahid Nazir – 1st Semester (MBA Col)

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The elements of this sample space are those industries which have declared dividends during the last two years. If any industry has not declared the dividend during either of the last two years will not belong to this sample space. It should be understood that a properly defined sample space considers or exhausts all possible outcomes and that there is no overlap among the elements within the space i.e. the events are mutually exclusive. Each time an experiment is conducted, one and only one outcome or event can occur.

BASIC RULES OF PROBABILITY Before discussing rules of probability, following concepts must be clarified.

i).

i)

Mutually exclusive and collectively exhaustive events

ii)

Compound events

iii)

Conditional probability

iv)

Independent events

MUTUALLY EXCLUSIVE & COLLECTIVELY EXHAUSTIVE EVENTS By mutually exclusive events (figure) we mean that the happening of one of them prevents or precludes the happening of the other. So if we toss a die and it shows 4, then the event of getting 4 precludes the event of throwing 1, 2, 3, 5, 6. Therefore the event of throwing 1, 2, 3, 4, 5, 6 on tossing a die are mutually exclusive. They are also collectively exhaustive as they together constitute the set of possible events (also called a sample space). Thus a set of events A1, A2, ………. An is mutually exclusive if Ai ∩ Aj = Ø (for any i ≠ j) and collectively exhaustive if E (the entire set) = A1 U A2 U A3 U …….. U An.

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A

ii).

B

COMPOUND EVENTS When two or more events occur in connection with each other, their simultaneous occurrence is called a compound event and the probability that the two or more events will all occur is called the “joint probability” of these events. The joint probability of two events is denoted as P(AB).

iii).

CONDITIONAL PROBABILITY The probability that is assigned to an event A when it is known that another event B has already occurred or that would be assigned to A if it were known that B had occurred is called the conditional probability of A given B and is denoted by P(A|B) (figure) and is given by P(A|B) = P(A ∩B) / P(B) if P(B) ≠ 0. A∩B

A

iv).

B

INDEPENDENT EVENTS

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If there are two or more events such that the occurrence of any one does not depend on the occurrence of any other, they are said to be independent. Thus if A and B are independent P (A|B)

=

P (A)

P (B|A)

=

P (B)

AADITIVE LAW OF PROBABILITY The probability that at least one of the several mutually exclusive events A1, A2, ………. An will occur is the sum of the probability of the occurrences of the individual events. Thus P(A1 U A2 U……… U An) = P(A1) + P(A2) + ……… + P(An) If an event A consists of n mutually exclusive and collectively exhaustive events, A1, A2, ………. An so that A occurs whenever any of these occur and vice versa, then A = A1 U A2 U……… U An So

P(A) = P(A1) + P(A2) + ……… + P(An)

ADDITION RULE Addition rule is used as a device for finding probabilities that can be expressed as P(A or B), the probability that either event A occurs or event B occurs (or they both occur) as the single outcome of the procedure. GENERAL RULE FOR COMPOUND EVENT When finding the probability that event A occurs or event B occurs, find the total number of ways A can occur and the number of ways B can occur, but find the total in such a way that no outcome is counted more than once. Zahid Nazir – 1st Semester (MBA Col)

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Formal Addition Rule P(A or B) = P(A) + P(B) – P(A and B) where P(A and B) denotes the probability that A and B both occur at the same time as an outcome in a trial or procedure. Intuitive Addition Rule To find P(A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, adding in such a way that every outcome is counted only once. P(A or B) is equal to that sum, divided by the total number of outcomes in the sample space. Definition Events A and B are disjoint (or mutually exclusive) if they cannot occur at the same time. (That is, disjoint events do not overlap.)

Diagram for events that are not disjoint

Diagram for disjoint events

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RULES FOR COMPLEMENTARY EVENT P(A) and P(Ā) are disjoint. It is impossible for an event and its complement to occur at the same time. Rules for the complementary events are: P(A) + P(Ā) = 1 P(Ā) = 1 – P(A) P(A) = 1 – P(Ā)

Diagram for the complement of event A

MULTIPLICATION RULE If the outcome of the first event A somehow affects the probability of the second event B, it is important to adjust the probability of B to reflect the occurrence of event A. The rule for finding P(A and B) is called the multiplication rule. P(A and B) = P(event A occurs in a first trial and event B occurs in a second trial)

Tree Diagrams A tree diagram is a picture of the possible outcomes of a procedure, shown as line segments emanating from one starting point. These diagrams are helpful if the number of possibilities is not too large.

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This figure summarizes the possible outcomes for a true/false followed by a multiple choice question. Note that there are 10 possible combinations.

Conditional Probability The probability for the second event B should take into account the fact that the first event A has already occurred. P(B|A) represents the probability of event B occurring after it is assumed that event A has already occurred (read B|A as “B given A.”) Formal Multiplication Rule P(A and B) = P(A) * P(B|A) Note that if A and B are independent events, P(B|A) is really the same as P(B). Intuitive Multiplication Rule When finding the probability that event A occurs in one trial and event B occurs in the next trial, multiply the probability of event A by the probability of event B, but be sure that the probability of event B takes into account the previous occurrence of event A. Zahid Nazir – 1st Semester (MBA Col)

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Applying the Multiplication Rule

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PRACTICAL STUDY OF THE ORGANISATION WITH RESPECT TO THE TOPIC

ORGANISATION:

GLAXOSMITHKLINE Pakistan Limited

SYSTEM STUDIED:

RISK MANAGEMENT SYSTEM

In GSK, the Risk Management System is used as proactive approach to eliminate / reduce the potential risks associated with their business. Probability theory is used extensively in Risk Management System for scoring the risks on the basis of likelihood and consequences.

Note :

This is only the overview of Risk Management System. Original documents could not be part of assignment due to their confidentiality.

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COMPANY INTRODUCTION: GlaxoSmithKline Pakistan Limited was created on January 1st 2002 through the merger of SmithKline and French of Pakistan Limited, Beecham Pakistan (Private) Limited and Glaxo Wellcome (Pakistan) Limited- standing today as the largest pharmaceutical company in Pakistan. As a leading international pharmaceutical company they make a real difference to global healthcare and specifically to the developing world. Company believe this is both an ethical imperative and key to business success. Companies that respond sensitively and with commitment by changing their business practices to address such challenges will be the leaders of the future. GSK Pakistan operates mainly in two industry segments: Pharmaceuticals (prescription drugs and vaccines) and consumer healthcare (over-the-counter- medicines, oral care and nutritional care). GSK leads the industry in value, volume and prescription market shares. Company proud of thier consistency and stability in sales, profits and growth. Some of their key brands include Augmentin, Panadol, Seretide, Betnovate, Zantac and Calpol in medicine and renowned consumer healthcare brands include Horlicks, Aquafresh, Macleans and ENO. In addition, companyis also deeply involved with our communities and undertake various Corporate Social Responsibility initiatives including working with the National Commission for Human Development (NCHD) for whom GSK was one of the largest corporate donors. GSK consider it their responsibility to nurture the environment we operate in and persevere to extend their support to our community in every possible way. GSK participates in year round charitable activities which include organizing medical camps, supporting welfare organizations and donating to/sponsoring various developmental concerns and hospitals. Furthermore, GSK maintains strong partnerships with non-government organizations such as Concern for Children, which is also extremely involved in the design, implementation and replication of models for the sustainable development of children with specific emphasis on primary healthcare and education.

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GSK’s MISSION STATEMENT Excited by the constant search for innovation, we at GSK undertake our quest with the enthusiasm of entrepreneurs. We value performance achieved with integrity. We will attain success as a world class global leader with each and every one of our people contributing with passion and an unmatched sense of urgency. Our mission is to improve the quality of human life by enabling people to do more, feel better and live longer. Quality is at the heart of everything we do- from the discovery of a molecule to the development of a medicine.

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RISK MANAGEMENT SYSTEM Risk management is an essential component of the system of internal control and governance and is regarded as good management practice throughout GSK. A systematic, standardized and effective approach to risk management is required in order to: • Establish a common language and protocols for communicating risks. • Ensure that responsibilities for managing risks are clearly stated, understood and accepted. • Establish appropriate mechanisms for communication, reporting and escalation of risks. • Ensure that business objectives are achieved.

SCOPE OF RISK MANAGEMENT PROCESS

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PROCESS STEP ACTIVITIES Following are the different steps involved in the risk management system: • Establish the Risk Management Organisation for the risk assessment area. • Identify, Record and Priorities Scored Risks. • Confirm and Approve Risk Mitigation plans. • Implementation, monitoring and of risk mitigation plans. • Governance and Maintenance.

Figure: Risk Management Process

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Probability theory comes into play when a risk is going to be scored (Analyse the risks). Risks are scored on the basis of likelihood and consequences.

INFORMATION STRUCTURE IN RMS • • • •

A Risk is the basic record. Risk requirements now split into three components. Mandated requirements to progress risks through workflow. A number of Risk Mitigation Plans may be attached to a Risk. A Risk must have at least one Risk Mitigation Plan. • A number of Action Plans may be attached to each a Risk Mitigation Plan. A Risk Mitigation Plan must have at least one Action Plan. • The diagram below depicts the structure of a Risk Record.

Risk

Risk Mitigation Risk Mitigation Risk Mitigation

Action Plans Action Plan(s)

Plan(s) Plan(s) Plan(s)

Approval

Approval

RISK SCORING • Risk scoring is subjective – there is no right or wrong answer it is based on personal judgement or consensus. • Review the consequence of a risk first and only when this is agreed – review the associated likelihood of the scored consequence.

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• The subjectivity on assessment of likelihood is inherently higher than that for consequence and influenced by individual perception, background, and local objectives - a team based approach is always used to reach consensus on likelihood. • Similar risks on different plants may have different scores because:
The impact to each plant is different from the same risk.
The risks are written in different ways / aggregated at different levels. • The key requirement for the risk management process is that the significant risks are identified managed appropriately – the precise scoring is a secondary consideration. • It is essential that risks within a risk assessment area are consistently scored and prioritised and a group view is required by the Quality management Process to avoid personal bias in scoring. • The scoring supports the prioritisation of risks but, even then, judgement is required where several risks all have the same score and decisions are required in terms of resource allocation. • Comparisons of numbers of risks on aggregation of risk assessment areas is of little value – any analysis and trending should focus on topics and not scores. • Differences in number and ratings of risks across risk assessment areas should be explored in terms of processes, resources and approach to generate them. • As with risk description, scoring is based on the current environment taking into account all controls.

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• A control can impact the consequence or likelihood. A control should be considered as something which impacts how severe a risk can become and not be limited to physical controls, written procedures or failsafe controls. • Risks should be assessed and scored from a GSK perspective. Hence, the consequence and likelihood Matrix (Appendix i) has been changed, to focus on the actions required by GSK with respect to the Regulators, rather than focus on the impact of the Regulators detecting risks e.g. observations. The likelihood captured in the risk management process is the likelihood of an event happening NOT the likelihood of detection e.g. by the regulators or internal auditors. • The timing of potential future audits relative to the risk being detected will not impact the score. • The frequency of manufacture using a particular process may impact the likelihood score. Note: Likelihood does not relate to how often a process is conducted but how often the risk associated with it is likely to occur. • If there is no historical example of a risk scenario being considered, but current controls would not stop the effect occurring then the likelihood is at least “possible” (3). • Risks must be considered against the criteria in each of the 3 consequence areas in turn and scored against the area with the highest consequence. • If there are several potential consequences with different root causes, then it may be necessary to separate these into separate risks on the register and score them individually.

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• The record of the consequence against which the risk is scored is in the “Area of Impact” column in the risk register. (Appendix ii) • The capture of the rationale for scoring should be encouraged and can be added in a column in the risk register or within the risk description.

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Appendix i

CONSEQUENCE AND LIKELIHOOD MATRIX CONSEQUENCES

LIKELIHOOD

Insignificant 1

Minor 2

Moderate 3

Major 4

Catastrophic 5

Almost certain 5

5

10

15

20

25

Likely 4

4

8

12

16

20

Possible 3

3

6

9

12

15

Unlikely 2

2

4

6

8

10

Rare 1

1

2

3

4

5

The outcome of the risk assessment process is a list of scored risks which can be prioritised based on scoring allowing decisions to be made on where resource and effort should be focused. There is a pre-determined Red, Amber, Green (RAG) analysis aligned to the Consequence and Likelihood Matrix (see above Appendix) which can be used to give initial guidance on banding of risks to support focus of activities i.e. Red = >10 Amber 5 – 9 Green <5

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Appendix ii

RISK MANAGEMENT SYSTEM (HOME PAGE)

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Appendix iii

RISK MANAGEMENT SYSTEM WORKFLOW

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Appendix iv

RISK IDENTIFICATION TOOLS
5 -Whys
Brainstorming
Surveys
Interviews
FMEA (Failure Mode Effect Analysis)
SWOT (Strengths, Weaknesses, Opportunities & Threats) analysis
PEST (Political, Economic, Socio-Cultural, Technological) analysis
Kaisen (Continuous Improvement)
GEMBA (Go and See)
Affinity & Fishbone diagrams
Reality Trees (Undesirable Effects (UDEs) for complex root cause analysis
Process flowcharts
Potential Problem Analysis (Kepnor Tregoe)
Benchmarking
Mind maps
IPO

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