2. Introduction A branch of mathematics concerned with the study of
randomness and uncertainity.
3. It is a measure of how often
a particular event will happen
if something is done
repeatedly.
If an event is certain to
happen then its probability is
1.
If an event is not certain to
happen then its probability is
0.
Probability is always between
0 and 1.
4. If you draw a card from a standard deck of cards, what is the
probability of not drawing a spade?
In a certain population, 10% of the people are rich, 5% are
famous, and 3% are both rich and famous. A person is
randomly selected from this population. What is the chance
that the person is
› not rich?
› rich but not famous?
› either rich or famous?
5. RANDOM
EXPERIMENT A random experiment is a process whose outcome is
uncertain.
Examples:-
Tossing a coin once or several times.
Picking a card or cards from a deck.
6. Sample Space
In probability theory,
the sample space of an
experiment or random
trial is the set of all
possible outcomes or
results of that
experiment.
7. The result of a random
experiment is called outcome.
Example:-
Tossing a coin and getting up
head or tail is an outcome.
Throwing a dice and getting a
no. between 1 to 6 is also an
outcome.
8. Any possible outcome of a
random experiment is called
an event.
The probability of an event,
denoted P(E), is the likelihood
of that event occurring.
Example:-
Performing an experiment is
called trial and outcomes are
termed as event.
9. FAVORABLE EVENT
The no. of outcome which result in
the happening of a desired event
are called favorable cases of the
event.
Example:-
In a single throw of a dice ,the no.
of favorable cases of getting an
odd no. are three.
10. Relative Frequency
Relative frequency is
another term for proportion;
it is the value calculated by
dividing the number of
times an event occurs by
the total number of times an
experiment is carried out.
11. In many situations, once more information
becomes available, we are able to revise
our estimates for the probability of further
outcomes or events happening.
For example, suppose you go out for
lunch at the same place with probability
0.9. However, given that you notice that
the restaurant is exceptionally busy, then
probability may reduce to 0.7.
12. The XVII century records the first use of
Probability Theory.
In 1654 Chevalier was trying to establish if such
an event has probability greater than 0.5.
Puzzled by this and other similar gambling
problems he called the attention of the famous
mathematician Blaise Pascal. In turn this led to an
exchange of letters between Pascal and another
famous French mathematician Pierre
de Fermat, this becoming the first evidence of
probability.
13. Emergence of
probability All the things that happened in the
middle of the 17th century, when
probability “emerged”:
Annuities sold to raise public funds.
Statistics of births, deaths, etc.,
attended to.
Mathematics of gaming proposed.
Models for assessing evidence and
testimony.
“Measurements” of the
likelihood/possibility of miracles.
“Proofs” of the existence of God.
