ITS MY POWER POINT

1. M RABEEK .S
1st M.Sc Microbiology
PROBABILITY & PROBABILITY DISTRIBUTION

2. INTRODUCTION
• Probability is the likehood 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.

4. SOME COMMON PROBABILITY PARLANCE IN
MEDICAL:
• A patient has a 50-50 chance of surviving a
certain operation.
• Another physician may say that she is 95%
certain that a patient has a particular disease.
• A public health nurse may say that nine times
out of ten a certain client will break an
appointment.

5. CONT….
• We measure the probability of occurrence of some event
by a number between zero and one.
• The more likely the event, the closer the prob. is to one
and more unlikely it is the closer the prob. to ‘0’.
• An event that can’t occur has a probability zero, and an
event that is certain to occur has a probability of one.
• Health sciences researchers continually ask themselves if
the result of their efforts could have occurred by chance
alone or if some other force was operating to produce the
observed effect

6. TWO VIEWS OF PROBABILITY:
• Objective
• subjective
• Objective Probability:
• Classical or a prior probability
• The relative frequency or a posterior

7. CLASSICAL PROBABILITY
• Definition-
• If an event can occur in N mutually
exclusive and equally likely ways, and if ‘m’ of
these possess a trait, E, the probability of the
occurrence of E is equal to m/N.
• Symbolically-
•
• P(E) – Prob. of E =P(E)=
m
N

8. CONT…
• If the process is repeated a large number of times, n ,
and if some resulting event with the characteristic E
occurs ‘m’ times, the relative frequency of occurrence
of E, m/n, will be approximately equal to the
probability of E. Symbolically P(E) = m/n
• Subjective Probability:
• Probability measures the confidence that a particular
individual has in the truth of a particular proposition.

9. CONT…
• This concept doesn’t rely on the repeatability of any
process.
• In fact, by applying this concept of probability, one
may evaluate the probability of an event that can only
happen once, for example, the probability that a cure
for cancer will be discovered within the next 10 years

10. LAWS OF PROBABILITY
• 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. TYPES OF PROBABILITY
• Marginal Probability;
• Union Probability;
• Joint Probability;
• Conditional Probability.

12. MARGINAL PROBABILITY
• 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. UNION PROBABILITY
• 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. JOINT PROBABILITY
• It is the third type of probability
• If E1 & E2 are two Events, then Joint probability is
denoted by P(E1∏E2 ).
• 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. CONDITIONAL PROBABILITY
• 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. APPLICATION OF PROBABILITY:
• Probability theory is applied in day to day life in risk
assessments and in trade on financial markets.
• Another Significant application of probability theory in
everyday life is reliability. Many consumer products, such
as automobiles and consumer electronics use reliability
theory in product design to reduce the probability of
failure.

17. PROBABILITY DISTRIBUTION

18. DISCRETE & CONTINUOUS RANDOM
DISTRIBUTIONS
• 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

19. 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.
Con

20. BINOMIAL PROBABILITY DISTRIBUTION
• 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).

21. POISSON DISTRIBUTION
• 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.

22. POISSON PROCESS CONDITIONS
• The event occur in a continuum of time & at a randomly
selected point & event either occurs or doesn’t occur.
• Whether the event occur or doesn’t 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.

23. NORMAL DISTRIBUTION
• 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.