probability theory in decision making

Zahid Nazir – 1st Semester (MBA Col)

Assignment No. 2

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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?


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


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


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

= 15/500 = 0.03

ii). 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

= 519 + 491 + 496 / 3000 = 0.502


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.


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


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


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) Mutually exclusive and collectively exhaustive events

ii) Compound events

iii) Conditional probability

iv) Independent events

i). 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.


A B

ii). 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

iv). INDEPENDENT EVENTS

A B


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.


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


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)

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.

Diagram for the complement of event A


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.

This figure summarizes the possible

outcomes for a true/false followed

by a multiple choice question.

Note that there are 10 possible

combinations.


Applying the Multiplication Rule


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.


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.


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.


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


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


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 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.

Risk Risk Mitigation

Plan(s) Risk Mitigation

Plan(s)

Risk Mitigation

Plan(s)

Action PlansAction Plan(s)

Approval Approval


• 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.


• 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.


• 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.

***********************


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


Appendix ii

RISK MANAGEMENT SYSTEM (HOME PAGE)


Appendix iii

RISK MANAGEMENT SYSTEM

WORKFLOW


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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probability theory in decision making

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