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Application of probability in
Daily life and in Civil
engineering
Presented by:
Engr Habib ur Rehman Chandio
Department of...
History
• The scientific study of probability is a modern development.
Gambling shows that there has been an interest in q...
History
• According to Richard Jeffrey, "Before the middle of the seventeenth century, the
term 'probable' (Latin probabil...
History
• The theory of errors may be traced back to Roger Cotes's Opera
Miscellanea (posthumous, 1722), but a memoir prep...
History
• The first two laws of error that were proposed both originated
with Pierre-Simon Laplace. The first law was publ...
History
• Daniel Bernoulli (1778) introduced the principle of the maximum
product of the probabilities of a system of conc...
History
• In the nineteenth century authors on the general theory included
Laplace, Sylvestre Lacroix (1816), Littrow (183...
Definition
• Probability is the measure of the likeliness that an event will
occur.[1] Probability is quantified as a numb...
Definition
• These concepts have been given an axiomatic mathematical
formalization in probability theory (see probability...
Applications
•
• Probability theory is applied in everyday life in risk assessment
and in trade on financial markets. Gove...
Applications
• The theory of behavioral finance emerged to describe the effect of
such groupthink on pricing, on policy, a...
Applications
• Another significant application of probability theory in everyday
life is reliability. Many consumer produc...
Applications
• Consider an experiment that can produce a number of results. The collection
of all results is called the sa...
Applications
• It can also be used to in real-time analysis of piezo electric current
transfer of pressure through electri...
Applications
• every two years 3 cyclones hit the coastal area of Andhra Pradesh
and Orissa states. If it is assumed that ...
Applications
• Two major applications of probability theory in everyday life are in risk assessment and in trade
on commod...
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Habib ur Rehman Chandio, Student at Wah Engineering College
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Application of probability in daily life and in civil engineering
1. 1. 1
2. 2. Application of probability in Daily life and in Civil engineering Presented by: Engr Habib
ur Rehman Chandio Department of Civil Engineering University of Wah, Wah Cantt.
3. 3. History • The scientific study of probability is a modern development. Gambling shows
that there has been an interest in quantifying the ideas of probability for millennia, but exact
mathematical descriptions arose much later. There are reasons of course, for the slow
development of the mathematics of probability. Whereas games of chance provided the
impetus for the mathematical study of probability, fundamental issues[clarification needed]
are still obscured by the superstitions of gamblers. Christiaan Huygens probably published
the first book on probability
4. 4. History • According to Richard Jeffrey, "Before the middle of the seventeenth century, the
term 'probable' (Latin probabilis) meant approvable, and was applied in that sense,
univocally, to opinion and to action. A probable action or opinion was one such as sensible
people would undertake or hold, in the circumstances." However, in legal contexts
especially, 'probable' could also apply to propositions for which there was good evidence. •
The sixteenth century polymath Gerolamo Cardano demonstrated the efficacy of defining
odds as the ratio of favourable to unfavourable outcomes (which implies that the probability
of an event is given by the ratio of favourable outcomes to the total number of possible
outcomes ). Aside from the elementary work by Cardano, the doctrine of probabilities dates
to the correspondence of Pierre de Fermat and Blaise Pascal (1654). Christiaan Huygens
(1657) gave the earliest known scientific treatment of the subject Jakob Bernoulli's Ars
Conjectandi (posthumous, 1713) and Abraham de Moivre's Doctrine of Chances (1718)
treated the subject as a branch of mathematics.See Ian Hacking's The Emergence of
Probability and James Franklin's The Science of Conjecture[full citation needed] for histories
of the early development of the very concept of mathematical probability. • .
5. 5. History • The theory of errors may be traced back to Roger Cotes's Opera Miscellanea
(posthumous, 1722), but a memoir prepared by Thomas Simpson in 1755 (printed 1756) first
applied the theory to the discussion of errors of observation.[citation needed] The reprint
(1757) of this memoir lays down the axioms that positive and negative errors are equally
probable, and that certain assignable limits define the range of all errors. Simpson also
discusses continuous errors and describes a probability curve
6. 6. History • The first two laws of error that were proposed both originated with Pierre-Simon
Laplace. The first law was published in 1774 and stated that the frequency of an error could
be expressed as an exponential function of the numerical magnitude of the error, disregarding
sign. The second law of error was proposed in 1778 by Laplace and stated that the frequency
of the error is an exponential function of the square of the error. The second law of error is
called the normal distribution or the Gauss law. "It is difficult historically to attribute that law
to Gauss, who in spite of his well-known precocity had probably not made this discovery
before he was two years old."
7. 7. History • Daniel Bernoulli (1778) introduced the principle of the maximum product of the
probabilities of a system of concurrent errors. • Adrien-Marie Legendre (1805) developed the
method of least squares, and introduced it in his Nouvelles méthodes pour la détermination
des orbites des comètes (New Methods for Determining the Orbits of Comets).[citation
needed] In ignorance of Legendre's contribution, an Irish-American writer, Robert Adrain,
editor of "The Analyst" (1808), first deduced the law of facility of error,
8. 8. History • In the nineteenth century authors on the general theory included Laplace,
Sylvestre Lacroix (1816), Littrow (1833), Adolphe Quetelet (1853), Richard Dedekind
(1860), Helmert (1872), Hermann Laurent (1873), Liagre, Didion, and Karl Pearson.
Augustus De Morgan and George Boole improved the exposition of the theory. • Andrey
Markov introduced[citation needed] the notion of Markov chains (1906), which played an
important role in stochastic processes theory and its applications. The modern theory of
probability based on the measure theory was developed by Andrey Kolmogorov (1931).
[citation needed] • On the geometric side (see integral geometry) contributors to The
Educational Times were influential (Miller, Crofton, McColl, Wolstenholme, Watson, and
Artemas Martin)
9. 9. Definition • Probability is the measure of the likeliness that an event will occur.[1]
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. A simple example is the toss of a fair coin. Since the two outcomes are
equally probable, the probability of "heads" equals the probability of "tails", so the
probability is 1/2 (or 50%) chance of either "heads" or "tails".
10. 10. Definition • These concepts have been given an axiomatic mathematical formalization in
probability theory (see probability axioms), which is used widely in such areas of study as
mathematics, statistics, finance, gambling, science (in particular physics), artificial
intelligence/machine learning, computer science, 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.
11. 11. Applications • • Probability theory is applied in everyday life in risk assessment and in
trade on financial markets. Governments apply probabilistic methods in environmental
regulation, where it is called pathway analysis. • A good example is the effect of the
perceived probability of any widespread Middle East conflict on oil prices—which have
ripple effects in the economy as a whole. An assessment by a commodity trader that a war is
more likely vs. less likely sends prices up or down, and signals other traders of that opinion.
Accordingly, the probabilities are neither assessed independently nor necessarily very
rationally.
12. 12. Applications • The theory of behavioral finance emerged to describe the effect of such
groupthink on pricing, on policy, and on peace and conflict. • The discovery of rigorous
methods to assess and combine probability assessments has changed society. It is important
for most citizens to understand how probability assessments are made, and how they
contribute to decisions.
13. 13. Applications • Another significant application of probability theory in everyday life is
reliability. Many consumer products, such as automobiles and consumer electronics, use
reliability theory in product design to reduce the probability of failure. Failure probability
may influence a manufacturer's decisions on a product's warranty. • The cache language
14.
15.
16.
17.
18.
model and other statistical language models that are used in natural language processing are
also examples of applications of probability theory.
14. Applications • Consider an experiment that can produce a number of results. The
collection of all results is called the sample space of the experiment. The power set of the
sample space is formed by considering all different collections of possible results. For
example, rolling a die can produce six possible results. One collection of possible results
gives an odd number on the dice. Thus, the subset {1,3,5} is an element of the power set of
the sample space of dice rolls. These collections are called "events." In this case, {1,3,5} is
the event that the dice falls on some odd number. If the results that actually occur fall in a
given event, the event is said to have occurred. • A probability is a way of assigning every
event a value between zero and one, with the requirement that the event made up of all
possible results (in our example, the event {1,2,3,4,5,6}) is assigned a value of one. To
qualify as a probability, the assignment of values must satisfy the requirement that if you
look at a collection of mutually exclusive events (events with no common results, e.g., the
events {1,6}, {3}, and {2,4} are all mutually exclusive), the probability that at least one of
the events will occur is given by the sum of the probabilities of all the individual events.
15. Applications • It can also be used to in real-time analysis of piezo electric current transfer
of pressure through electric impulses due to strain and stress concentration at localized spots.
Like this the applications are many with the modern Civil Engineering taking a huge leap
into modernity with the aid of electronics, it becomes more fun and highly technical to use
probability and Statistics in Civil Engineering • It can be used in amplification and fine
tuning of resonant frequency wave identification in Wind Structures, to monitor remotely the
structural health of a structure (such as a bridge, tall building, dams etc).
16. Applications • every two years 3 cyclones hit the coastal area of Andhra Pradesh and
Orissa states. If it is assumed that the cyclone hitting the coastal areas follows Poisson
distribution then what is the probability of two cyclones crossing the coastal area of Andhra
Pradesh and Orissa in the next two years • It is useful in risk assessment • it can be used for
random decrement analysis. • In earth quake engineering, in a specific time interval the
probability of occurrence of an earth quake at a particular fault follows Poisson distribution.
Occurrence of cyclones in a particular time period follows Poisson distribution.
17. Applications • Two major applications of probability theory in everyday life are in risk
assessment and in trade on commodity markets • probability theory in everyday life is
reliability. Many consumer products, such as automobiles and consumer electronics, utilize
reliability theory in the design of the product in order to reduce the • a toss of a coin may
result in either a head or a tail. Also, the sex of a new-born baby may turn out to be male or
female. In these cases, the individual outcomes are uncertain. With experience and enough
repetition, however, a regular pattern of outcomes can be seen (by which certain predictions
can be made). • In the twentieth century probability is used to control the flow of traffic
through a highway system • a telephone interchange, or a computer processor; find the
genetic makeup of individuals or populations; figure out the energy states of subatomic
particles; Estimate the spread of rumors; and predict the rate of return in risky investments. •
When a meteorologist states that the chance of rain is 50%, the meteorologist is saying that it
is equally likely to rain or not to rain. If the chance of rain rises to 80%, it is more likely to
rain. If the chance drops to 20%, then it may rain, but it probably will not rain.
18. Thank you … … for paying attention
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