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.
It gives detail description about probability, types of probability, difference between mutually exclusive events and independent events, difference between conditional and unconditional probability and Bayes' theorem
How to Make a Field invisible in Odoo 17Celine George
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http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
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How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
2. Basic Terms of Probability
In probability, an experiment is any process that can be repeated in which the
results are uncertain.
A simple event is any single outcome from a probability experiment.
Sample space is a list of all possible outcomes of a probability experiment.
An event is any collection of outcomes from a probability experiment.
3. Example
Experiment : Tossing a coin
Sample Space: { Head, Tail)
Event: (Only Head wants) : {Head}
4. Probability
The probability of an event, denoted P(E), is the likelihood of that event occurring.
The Probability of an event :
P(Event) =
𝑇ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑖𝑡 𝑐𝑎𝑛 ℎ𝑎𝑝𝑝𝑒𝑛
𝑇ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
5. Example
When a coin is tossed, there are two possible outcomes: Heads and Tails
P(Heads) = ½
When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.
P(1) = 1/6.
6. Properties of Probability
The probability of any event E, P(E), must be between 0 and 1 inclusive. That is, 0
< P(E) < 1.
If an event is impossible, the probability of the event is 0.
If an event is a certainty, the probability of the event is 1.
If S = {e1, e2, …, en}, then P(e1) + P(e2) + … + P(en) = 1.
7. Three methods for determining
Probability
Classical method
Empirical method
Subjective method
8. Classical Method
The classical method of computing probabilities requires equally likely outcomes.
If an experiment has n equally likely simple events and if the number of ways that
an event E can occur is m, then the probability of E, P(E), is
9. Example for classical method
Let us suppose a bag of balls contains 6 brown balls, 15 yellow balls, 5 red balls,
20 orange balls, 11 blue balls, and 4 green balls. Suppose that a ball is randomly
selected.
What is the probability that it is brown?
P(Brown) = 6/61
10. Limitations of Classical method
Classical method fails if the number of outcomes of the random experiment is
infinite.
If the various outcomes of random experiment are not equally likely.
If the actual number of possible outcomes is not known.
11. Empirical method
The probability of an event E is approximately the number of times event E is
observed divided by the number of repetitions of the experiment.
The empirical probability, also known as relative frequency.
The empirical approach to probability is based on law of large numbers.
So to achieve more accuracy in the result, collect more observations which provide
more accurate estimate of the probability.
12. Example for Empirical method
A coin is thrown 100 times out of which head appears 12 times. Find the
experimental probability of getting the head?
The coin is thrown 100 times. So total number of trails =100
Given head occurs 12 times. So the number of times the required event occurs =
12
Therefore probability of getting the event of head =
12
100
= 0.12
13. Subjective Probability
Subjective probabilities are probabilities obtained based upon an educated guess.
A subjective probability describes an individual's personal judgment about how
likely a particular event is to occur.
A person's subjective probability of an event describes his/her degree of belief in
the event.
For example, there is a 10% chance of rain tomorrow.