stats

1. PROBABILITY
Ms. K. Lavanya
MSc(N)-CHN
Associate Professor

2. Random:
• If the outcome is uncertain, we will say its all Random.
• Means it is not in our control
• Depends upon many factors
• An outcome is the result of an experiment (or) any other situation involving
uncertainty.
• An event is a collection of outcomes of an experiment.

3. Uncertainty & Probability
• Uncertainty when there is no access to the whole truth. (Environment/incomplete
data/noise).
• In the Experts
• Inherent in the domain
• In knowledge representation
• As to the accuracy & availability of knowledge.
Probability is not about numbers It is about the structure of reasoning. _ Glenn
shafer

4. Origin of Probability
• From Games to Chance:
• In 17th
century French gamblers asked Blaise Pascal & Pierre Deformat then well Known
pioneers in mathematics for help in gambling.
• In 18 & 19 centuries studies is astronomy led to further advances in probability.
• In 20th
century probability is used to:
- Control the flow of traffic through the highway system.
- Find the genetic makeup of individuals or population.
- Estimate the spread of rumors
- Predict rate of return in risky investments.

5. Occurences:
• Predictable Occurences: The outcome is unique or certain and the other
in which the outcome is not unique and it may be one of the many outcomes
this is called predictable occurences.
• Eg: Energy is equal to mass of the particle into square of its velocity.
(e=mv2).
• Unpredictable Occurences: Use of coin is may limit to Head or Tail.
The sex of newborn baby, may be the outcome is male or female.

6. Regular pattern:
• With experience & enough repetition regular pattern of outcomes can be seen
by which certain predictions can be made.
Example: Repeat to using a coin 100 or more result. A pattern of 50 heads (or)
50 tails coin should be unbiased.

7. Random Phenomenon:
• An event (or) phenomenon is random if individual outcomes are uncertain.
BOT:
A regular distribution of relative frequencies in a large number of repetitions
can be observed.

8. Trail & Event
• After throwing a die one can get 1 or 2 or 3 or 4 or 5 or 6. Here throwing a die
is a “trial”. It will be realized that if this trial is repeated under essentially
identical conditions, it will not give unique results but will result in any one
of the six possible outcomes. The various outcomes are known as events.
• Eg: Drawing three cards from a pack of well shuffled cards is a trial and
getting a spade queen, diamond ace or heart king are events.

9. Exhaustive Event:
• The total number of possible outcomes in any trial is
known as exhaustive events.
Eg: In a match there are three exhaustive events namely
win, loss or a draw. In a case of throwing two dice together
the exhaustive events are 36.

10. Favorable Events:
• One must Know that in discussing probability the terms “favorable & success” are
not used with their literal meaning. It won’t be rare to see that ones success is others
failure in a game of chance.
• Favorable can mean that a refrigerator is out of order or there is a case of polio
myelitis due to vaccine failure.
• The number of cases favorable to an event in a trial is the number of outcomes which
entail the happening of the event Eg: In tossing a coin, the number of cases favorable
for getting a head is 1 and for getting a tail is 1. Similarly in throwing two dice the
number of cases favorable to getting a sum of 8 is –(2,6), (3,5), (4,4), (5,3) and (6,2).

11. Mutually Exclusive Events:
• Events are said to be mutually exclusive or incompatible if the
happening of any one of them precludes the happening of all
others i.e., no two or more of them can happen simultaneously in
the same trial.
• In drawing a single card from a pack one can see that from ace to
lowest card of every type i.e., spade, diamond, heart or club each
card is unique in nature. Once you get a diamond queen you can
not get anything else.

12. Equally Likely Events:
• Outcomes of a trial are said to be equally likely if taking into consideration all
the relevant evidences, there is no reason to expect one in preference to other
Eg: when we toss a coin, getting head or tail are equally likely events.

13. Independent Events:
• Two events E1 & E2 are independent if the occurrence of E1 does not affect
the probability of E2 & vice versa i.e., occurrence of E2 does not affect the
probability of E1.
Eg: Independent event = In the set of 52 cars of what is the probability to Ace
P (Ac)= 4/52, P (Ac)=3/51.

14. Dependent Events:
• An event E2 is said to be dependent on an event E1 if occurrence of E1 affects
the probability of the occurrence of E2.
Eg: If the draw one of Ace if card is not replaced.
P(Ace)=4/52
P (Ace)= 3/51