The document provides an introduction to probability, defining it as the chance of an event occurring, expressed as a ratio of favorable outcomes to total possible outcomes. It discusses key concepts such as random experiments, random variables, different types of events (like mutually exclusive and independent events), and probability distributions. Additionally, it contrasts objective and subjective approaches to probability assessment.

1. PROBABILITY

2. INTRODUCTION
What is a PROBABILITY?
- Probability is the chance that some event will happen
- It is the ratio of the number of ways a certain event can occur to the number
of possible outcomes
- A number that represents the chance that a particular event will occur for a
random variable.
- Eg: Odds of winning a lottery, chance of rolling a seven when rolling two dice,
percent chance of rain in a forecast

3. • Probability - expressed in terms of percentage (generally)
• Expressed in terms of fractions (mathematically)
• Probability of occurrence – between zero and one
Random Experiment:
• Any well – defined process of observing a given chance phenomena
through a services of trials that are finite or infinite and each of which
leads to a single outcome is known as a random experiment.

4. • Example: Drawing a card from a pack of 52 cards. This is also a
chance phenomena with only one outcome.
• A random experiment is different from experiments under control
conditions because the observation in a random experiment involves
chance phenomena and is not performed under controlled conditions.
• Random variable – numerical quantity that takes on different values
depending on chance

5. BASIC TERMS
• Experiment: Set or Trial / Sets or Trial in which an operation is
conducted to discover an unknown behaviour
• Outcome: Result of the experiment
• Population – the set of all possible outcomes for a random variable (
only hypothetical population, not a population of people)

6. BASIC TERMS
• An event – an outcome or set of outcomes for a random variable
• Random variable – numerical quantity that takes on different values
depending on chance
• Population – the set of all possible outcomes for a random variable (
only hypothetical population, not a population of people

7. THEOREMS OF PROBABILITY
Probability Theorems
Addition
Theorem
Multiplication
Theorem
Bayes’
Theorem
Mutually
Exclusive
Events
Partially
Overlappin
g Events
Dependent
Variables
Independent
Variables

8. Exhaustive Events:
The total number of all possible elementary outcomes in a random
experiment is known as ‘exhaustive events’. In other words, a set is said to be
exhaustive, when no other possibilities exists.
Favorable Events:
The elementary outcomes which entail or favor the happening of an event is
known as ‘favorable events’ i.e., the outcomes which help in the occurrence of
that event.

9. Mutually Exclusive Events:
Events are said to be ‘mutually exclusive’ if the occurrence of an event
totally prevents occurrence of all other events in a trial.
In other words, two events A and B cannot occur simultaneously.
Complementary Events:
Let E denote occurrence of event. The complement of E denotes the non
occurrence of event E. Complement of E is denoted by ‘ ’
Ē

10. Equally likely or Equi-probable Events:
Outcomes are said to be ‘equally likely’ if there is no reason to expect one
outcome to occur in preference to another.
i.e., among all exhaustive outcomes, each of them has equal chance of
occurrence.
Independent Events:
Two or more events are said to be ‘independent’, in a series of a trials if the
outcome of one event is does not affect the outcome of the other event or vise
versa.

11. Discrete Distribution:
Random Variable can take only limited number of values. Ex: No. of
heads in two tosses.
Continuous Distribution:
Random Variable can take any value. Ex: Height of students in the class.

12. Probability Distributions:
• They are described in the form of a graph, table, or formula the
probable behaviour of a random variables events in an experiment.
• Two types of Random variables and two types of PD to describe
them.
Discrete Random Variable:
It is one whose events are integer values starting with 0,1,2 and so on
to some positive value that can be counted

13. APPROACHES TO PROABILITY ASSESSMENT
TWO VIEWS OF PROBABILITY
Objective approach to Probability:
a) Frequency Theory
b) The Principle of insufficient Reason
Subjective approach to Probability