This document discusses the practical applications of probability theory in various domains. It begins by defining key probability concepts like events, random experiments, and non-random experiments. It then provides examples of applying probability to weather forecasting, calculating statistics like fatality and mortality rates, and assessing odds in games involving chance. The document emphasizes that while probability is useful for modeling outcomes, there will always be an uncertain element that cannot be perfectly predicted.

1. Presented by: Adrija Ganguly Roll no.:04
CSE 1A

2. The word probability derives from the Latin probabilitas, which can
also mean "probity", a measure of the authority of a witness in a legal
case in Europe, and often correlated with the witness's nobility.
Probability is the measure of the likelihood that an event will occur. Probability
is quantified as a number between 0 and 1 (where 0 indicates impossibility and
1 indicates certainty). The higher the probability of an event, the
more certain we are that the event will occur.

3. EVENT: In probability theory, an event is a
set of outcomes of an experiment (a subset of
the sample space) to which a probability is
assigned.
RANDOM EXPERIMENT: An
experiment whose outcome
cannot be predicted with
certainty, before the experiment
is run.
NON-RANDOM
EXPERIMENT: An experiment
whose outcome may or may not
be predicted before the
experiment is run.
TERMS IN PROBABILITY WHICH HAS THEIR
APPLICATION IN REAL LIFE

4. EVENT NON-
RANDOM
PROPERTY
RANDOM
PROPERTY
Weather Seasonal change,
local climate
Perspiration,
temperature on
specific days
Car accidents Safe or unsafe
driving practices
Specific cars or
conditions met on
the road
Class grades Amount of study
and preparation
Appearance of
specific questions
on test
Customers at
mall
Hours open, time
of day
Specific pattern
of customer
arrival
State lottery Decisions about
games offered,
prizes
Numbers drawn
or winning
pattern of tickets

5. Well, there are many practical applications of Probability.
Some of them are:
1. Communication ( In order to estimate the noise in the channel
for calculating the S/N ratio)
2. Weather forecasting.
3. Calculating statistics ( eg. Life expectancy and population
index)
4. Games (eg.Gambling etc).

6. Planning Around the Weather
Nearly every day we use probability to plan around the weather.
Meteorologists can't predict exactly what the weather will be, so they
use tools and instruments to determine the likelihood that it will rain,
snow or hail.
For example, if there's a 60-percent chance of rain, then the weather
conditions are such that 60 out of 100 days with similar conditions, it
has rained. We may decide to wear closed-toed shoes rather than
sandals or take an umbrella to work.

7. Calculating Statistics
FATALITY RATE: In epidemiology, a case fatality risk (CFR) —
or case fatality rate, case fatality ratio or just fatality rate — is the
proportion of deaths within a designated population of "cases" (people with a
medical condition), over the course of the disease.
MORTALITY RATE: Mortality rate is typically expressed in units of
deaths per 1,000 individuals per year; thus, a mortality rate of 9.5 (out of
1,000) in a population of 1,000 would mean 9.5 deaths per year in that entire
population, or 0.95% out of the total.

8. Games and Recreational Activities
We use probability when you play board, card or video games that
involve luck or chance. You must weigh the odds of getting the cards you
need in poker or the secret weapons you need in a video game. The
likelihood of getting those cards or tokens will determine how much risk
you're willing to take.
For example, the odds are 46.3-to-1 that you'll get three of a kind in your
poker hand -- approximately a 2-percent chance -- according to Wolfram
Math World. But, the odds are approximately 1.4-to-1 or about 42 percent
that you'll get one pair. Probability helps us assess what's at stake and
determine how you want to play the game.

9. Luck is generally used to describe success or failure
apparently brought by chance rather than through one’s
own actions. The definition of
luck(or chance) varies by the
philosophical, religious,
mystical, and emotional
context of the one interpreting
it. So as we say it,
LUCK IS PROBABILITY TAKEN PERSONALLY!
A DIFFERENT ASPECT OF PRACTICAL APPLICATION OF
PROBABILITY : BEING LUCKY

10. In conclusion, we think although probability has a lot of
practical applications, it’s very important to remember that
we’ll never have probabilities in the clear-cut way a casino
has them.
There will always be some
degree of subjective belief
we’ll need to incorporate, at
least for the near future. So it
has to be kept in mind that
while our projection systems
and statistical analysis continue to improve and become
more accurate, there will always be an element we
can’t model.