This document discusses key concepts in probability. It defines basic terms like experiment, sample space, event, and probability. It provides examples of calculating probability for coin tosses and dice rolls using the classical method of dividing the number of ways an event can occur by the total number of possible outcomes. The document also discusses limitations of the classical method and introduces the empirical and subjective methods of determining probability based on observed frequencies and personal judgment respectively.
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.
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
Probability is the way of expressing knowledge of belief that an event will occur on chance.
Did You Know? Probability originated from the Latin word meaning approval.
Make use of the PPT to have a better understanding of Probability.
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
Probability is the way of expressing knowledge of belief that an event will occur on chance.
Did You Know? Probability originated from the Latin word meaning approval.
Make use of the PPT to have a better understanding of Probability.
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The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
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Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
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.
