Probability is the mathematics of chance that can be expressed as a fraction, decimal, or percentage. It provides the likelihood that a given event will occur based on the number of possible outcomes of an experiment. The probability of any single event must be between 0 and 1, and the sum of probabilities of all events must equal 1. Common experiments used to demonstrate probability include tossing a coin, rolling a die, and tossing two coins simultaneously, with the outcomes and events defined for each. The theoretical probability of an event is calculated by dividing the number of outcomes for that event by the total number of possible outcomes.
History behind the
development of the concept
In 1654, a gambler Chevalier De Metre approached the well known Mathematician Blaise Pascal for certain dice problem. Pascal became interested in these problems and discussed it further with Pierre de Fermat. Both of them solved these problems independently. Since then this concept gained limelight.
Basic Things About The Concept
Probability is used to quantify an attitude of mind towards some uncertain proposition.
The higher the probability of an event, the more certain we are that the event will occur.
Basic probability Concepts and its application By Khubaib Razakhubiab raza
introduction of probability probability defination and its properties after that difference between probability and permutation in the last Discuss about imporatnace of Probabilty in Computer Science
History behind the
development of the concept
In 1654, a gambler Chevalier De Metre approached the well known Mathematician Blaise Pascal for certain dice problem. Pascal became interested in these problems and discussed it further with Pierre de Fermat. Both of them solved these problems independently. Since then this concept gained limelight.
Basic Things About The Concept
Probability is used to quantify an attitude of mind towards some uncertain proposition.
The higher the probability of an event, the more certain we are that the event will occur.
Basic probability Concepts and its application By Khubaib Razakhubiab raza
introduction of probability probability defination and its properties after that difference between probability and permutation in the last Discuss about imporatnace of Probabilty in Computer Science
Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.[note 1][1][2] The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ('heads' and 'tails') are both equally probable; the probability of 'heads' equals the probability of 'tails'; and since no other outcomes are possible, the probability of either 'heads' or 'tails' is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event.
2. Probability is the mathematics
of chance.
It can be written as a fraction,
decimal, percent, or ratio.
It tells us a result with
which we can expect an event
to occur
3. – an operation which
produces well-defined outcomes is called
an experiment .
– an experiment
when repeated under identical condition,
does not produce the same result, is
known as a random experiment.
– a result of some activity or
experiment is known as outcome.
– the collection of some or all
possible outcomes of an experiment is
called an event.
4. Value is between 0 and 1.
Sum of the probabilities of all
events is 1
Probability is the numerical
measure of the likelihood
that the event will occur.
Certai
n
Impossi
ble
50/50
.5
1
0
5. S.N Experiment Outcomes Some events
1 Tossing a coin Head(h)
Tail (T)
•H is the event of getting a head.
T is the event of getting a tail.
2 Rolling a dice 1,2,3,4,5,6 Getting an odd no is the event containing 1,3,5.
Getting a prime number is the event containing 2,3,5.
Getting a number greater than 5 is the event
containing 6 and so on.
3. Tossing two
coins
simultaneously.
HH,HT,TH,TT HH is the event of getting head on each coin.
HT is the event of getting head on 1st coin and tail on
2nd coin
TH is the event of getting tail on 1st coin and Head on
2nd coin.
TT is the event of getting tail on each coin.
.
6.
7.
8. The probability of an event , E.
Number of Event Outcomes
P(E) =
Total Number of Possible Outcomes in S
Each of the outcomes in the sample
space are random and equally likely
to occur .
E.g p( ) = 2/36 = 1/18
(There are 2 ways to get one 6 and
the other 4)
9. There are three types of probability
1. Theoretical Probability
Theoretical probability is used
when each outcome in a sample
space is equally likely to occur.
P(E) ==
Number of Event Outcomes
Total Number of Possible Outcomes in S
The Ultimate probability formula