2. Probability is the likelihood or chance that a particular
event will or will not occur; The theory of probability provides a
quantitative measure of uncertainty of occurrence of different
events resulting from a random experiment, in terms of quantitative
measures ranging from 0 to 1; 3. Experiment: it is a process which
produces outcomes; Example, tossing a coin is an experiment; an
interview to gauge the job satisfaction levels of the employees in
an organization is an experiment; Event: it is the outcome of an
experiment; Example, if the experiment is to toss a fair coin, an
event can be obtaining a head; if an event has a single possible
outcome, then it is a simple (or elementary) event; a subset of
outcomes corresponding to a specific event is called an event
space. 4. Independent & Dependent Events: two events are said
to be independent, if the occurrence or non-occurrence of one is
not affected by the occurrence or non-occurrence of the other; vice
versa Mutually Exclusive Events: two or more events are said to be
mutually exclusive if the occurrence of one implies that the other
cannot occur; if X and Y are mutually exclusive, then P(XY)=0
Sample Space: denoted by S; it is the set of all possible outcomes
in an experiment; 5. Classical/ Prior Approach; Relative
sequence/Empirical Approach;& Subjective/Intuitive/Judgmental
Approach. 6. This approach happens to be the earliest; This school
of thought assumes that all the possible outcomes of an experiment
are mutually exclusive & equally likely; If there are a
possible outcomes favorable to the occurrence of Event E, & b
possible outcomes unfavorable to the occurrence of Event E &
all these possible outcomes are equally likely & mutually
exclusive, then the probability that the event E will occur,
denoted by P(E), is P(E)= Number of outcomes favorable to
occurrence of E Total number of outcomes 7. This approach has two
characteristics: a. The subjects refers to fair coins, fair decks
of cards; but if the coin is unbalanced or there is a loaded dice,
this approach would offer nothing but confusion; b. In order to
determine probabilities, no coins had to be tossed, no cards
shuffled, i.e. no experimental data were required to be collected;
8. This method uses the relative frequencies of past occurrences as
the basis of computing present probability; hence it is based on
experiments conducted in the past; If an Event E has occurred r
number of times in a series of n independent trials;, all under
uniform conditions, then the ratio of r gives the probability of
Event E provided n is sufficiently large: P(E)= r = favorable
trials n total of trials 9. This approach is based on the intuition
of an individual; This is not a scientific approach; It is based on
accumulation of knowledge, understanding and experience of an
individual; 10. For any event probability lies between 0 & 1;
It is represented in percentages, ratios, fractions; Each event has
a complementary event i.e. P(E1) + P(E1) =1 11. Marginal
Probability; Union Probability; Joint Probability; Conditional
Probability. 12. It is the first type of probability; A marginal or
unconditional probability is the simple probability of the
occurrence of an event; Denoted by P(E) where E is some event;
P(E)= Number of outcomes favorable to occurrence of E Total number
of outcomes 13. Second type of probability; If E1 & E2 are two
Events, then Union probability is denoted by P(E1 U E2 ); It is the
probability that Event E1 will occur or that Event E2 will occur or
both Event E1 & Event E2 will occur; For example, union
probability is the probability that a person either owns a Maruti
800 or Maruti Zen. For qualifying to be part of the union, a person
has to have atleast one of these cars 14. It is the third type of
probability; If E1 & E2 are two Events, then Joint probability
is denoted by P(E1E2 ); It is the probability of the occurrence of
Event E1 and Event E2; For example, it is the probability that a
persons owns both a Maruti 800 & Maruti Zen; for joint
probability, owning a single car is not sufficient; 15. It is the
fourth type of probability; Conditional Probability of two Events
E1 & E2 is generally denoted by P(E1/E2); It is probability of
the occurrence of E1 given that E2 has already occurred;
Conditional probability is the probability that a person owns a
Maruti 800 given that he already has a Maruti Zen; 16. Used to
estimate union probability; If there are two Events E1 & E2,
then the general rule of addition is given by: P(E1 or E2) = P(E1)
+ P(E2) P (E1 & E2); P(E1 U E2) = P(E1) + P(E2) P (E1E2);
Special Rule of addition for mutually exclusive: P(E1 or E2) =
P(E1) + P(E2); P(E1 U E2) = P(E1) + P(E2); 17. Used to estimate
joint probability and also conditional probability; If there are
two Events E1 & E2, then the general rule of multiplication is
given by: P(E1 & E2) = P(E1) . P(E2 /E1); P(E1 E2) = P(E1) .
P(E2 /E1) ; Special Rule of multiplication for independent events:
P(E1 & E2) = P(E1) . P(E2); P(E1 E2) = P(E1) . P(E2); 18. Bayes
theorem was developed by Thomas Bayes. In fact, Bayes theorem is an
extended use of the concept of conditional probability; The law of
conditional probability is given by: P(E1/E2) = P(E1 E2) = P(E1) .
P(E2 /E1) P(E2) P(E2) 19. A random variable is a variable which
contains the outcome of a chance experiment; for example, in an
experiment to measure the number of customers who arrive in a shop
during a time interval of 2 minutes; the possible outcome may vary
from 0 to n customers; these outcomes (0,1,2,3,4,n)are the values
of the random variable. These random variables are called discrete
random variables 20. In other words , a random variable which
assumes either a finite number of values or a countable infinite
number of possible values is termed as Discrete Random variable On
the other hand, random variables that assumes any numerical value
in an interval or can take values at every point in a given
interval is called continuous random variable. For example,
temperatures recorded for a particular city can assume any number
like 32O F, 32.5O F 35.8O F Experiment outcomes which are based on
measurement scale such as time, distance, weight & temperature
can be explained by Continuous Random variable 21. Most commonly
used & widely known distribution among all discrete
distributions. It is a sequence of repeated trials, called
Bernoulli Process which is characterized by: 1. Only two mutually
exclusive outcomes are possible;( one is referred to as success
& the other as failure) 2. The outcomes in a series of
trials/observation constitute independent events; 3. Probability of
success (p) or failure (q) is constant over a number of trials; 4.
The number of events is discrete & can be represented by
integers(0,1,2,3,4,onwards) 22. P(X)= nCxpxqn-x where n= total
number of trials x = Designated value p= probability of success q=
probability of failure nCx= n!___ x!(n-x)! 23. It is named after
the famous French Mathematician Simeon Poisson; It is also a
discrete distribution; but there are a few differences between
Binomial & Poisson distributions. For a given number of trials
the binomial distribution describes a distribution of two possible
outcomes: either success or failure whereas Poisson focuses on the
number of discrete occurrences over an interval. It is widely used
in the field of managerial decision making; widely used in queuing
models 24. The event occur in a continuum of time & at a
randomly selected point & event either occurs or doesnt occur;
Whether the event occur or doesnt occur at a point, it is
independent of the previous point where the event may have occurred
or not; The probability of occurrence of events remains
same/constant over the whole period or throughout the continuum;
25. P(x/)= x e-x! (greek letter lambda) =mean/average e (constant)=
2.71826 x is a random variable(designated number) 26. It is the
most commonly used distribution among all probability
distributions; It has a wide range of practical application
example, where the random variables are human characteristics such
as height, weight, speed, IQ scores; Normal distribution was
invented in the 18th century; 27. The curve of normal distribution
is symmetrical/ mesokurtic; The mean, median & mode are
identical; The two tail of normal curve asymptotic; Curve is
unimodal; The total area under normal distribution is 100% &
the distribution is as follows: +1 = 68% +2 =97% +3 = 99.7% Z=
x-
