Decision Science_2.docx

Decision Science
June 2022 Examination
Ans 1.
Introduction
In probability theory, a probability space is shown as a tree diagram. The probability diagram is
based on "trees" of conditional probabilities. Coin flips and card draws, for example, have
outcomes that are entirely dependent on luck. The probability tree diagram will be
incomprehensible if you don't understand this first. Using this method, it is possible to estimate
the likelihood of a given event happening. A one in a million probability is the most probable
result. More complex divisions may be represented by sibling nodes. Decision trees may be used
by statisticians. A simpler way to show the links between several options is via the use of a decision
tree diagram, which is an illustration of a probability tree diagram. Constructing conditional
statements is simple using this approach.
Concept and Application
The city of Srinagar has three airports, making it easy to go around. The country's three biggest
airlines are responsible for around half of all domestic flights. Airlines fly above much of the city,
keeping a careful watch on the situation. Only three airlines generate more than 80% of their
overall income, according to a study.
Probability theory may be shown via a tree diagram. The visual representation of randomness and
conditional probability provided by probability trees is simple to comprehend. A faulty coin flip
may have launched this chain reaction. It's possible that the card you draw will remain in the spot
where you placed it, regardless of how random your estimate was. It is possible to assess the
likelihood of a certain event occuring at each node of a chance tree diagram. There will always be
a one-time opportunity cost for the main node as a consequence of this, and it is feasible to design
unique and complete walls using siblings. A subsequent event may occur if a node is given the

opportunity to occur after an earlier event. anything that happened in the past. A node's parents
and products have the same probability of occurring as the node itself.
A selection tree is used to represent any other statistical data.
It is possible to make better judgments if you use probability and decision trees. This strategy
makes it easy to determine the extent of an event's effect and harm. In mathematics, the use of
conditional change expressions is commonplace.
Amira's value may be estimated using the opportunity diagram. Here is a table containing the data
shown in the opportunity tree visual.
The scheduled flights of the airline Amira are represented by Event A.
Event B shows all of the flights that the airline Biyas has scheduled.
Event C shows the last flights of Chinar.
The probability of the flights is:
P (Amira) = 0.50
P (Biyas) = 0.30

P (Chinar) = 0.20
When it comes to the probability of the future,
P (E|Amira)= 0.80
P (E|Biyas) = 0.65
P (|Chinar) = 0.40
Flights booked for Airline A account for 50% of all flights. Airline B flies 30% of the planned
flights, whereas airline C operates 20% of them. Eighty percent, sixty-five percent, and forty
percent of the time, they will all be on time for work.
Let us have a look at it.
The forthcoming flights of Airline A are listed in Event A.
Flight schedules for Airline B are included in Event B.
For the time period C, Airline C has planned flights.
Using the letter E, we indicate that the flight arrived on schedule.
We need to find out how probable it is that the aircraft leaving Srinagar departed from Amira.
For the same reason, P (A|E) must be calculated.
Putting the values received from the posterior chance into the Bayes's law formulation, it presents
with,
P(the flight is by A | the flight is on-time) =

P(A∣E) = P(E∣A)×P(A)
P(E∣B)×P(B)+P(E∣C)×P(C)P(E∣A)×P(A)
P ((A|E)= (0.80*0.50)/(0.80*0.50)+(0.65*0.30)+(0.40*0.20)= 0.59259
Hence, the flight that left Srinagar to belong to airline Amira stands at 0.5926.
= 59.26%.
Utilizing a chance tree diagram, it is possible to calculate the probability of a large number of
events happening simultaneously The possibility of different outcomes happening may be shown
graphically if all parties are on an equal footing. More sophisticated probability calculations may
be completed in less time using this method. In certain cases, it may be difficult to determine
whether to multiply or upload the probability. There may be a need for more opportunities in order
to speed up the procedure.
Conclusion
In order to get a sense of how likely it is that various occurrences will occur in the near future, you
may utilise probability trees. [*] It allows users to compare the consequences of multiple distinct
adjustments all at once using the software they've downloaded. To do this method, you don't need
these equations. Probabilistic computations may make you unclear whether to multiply or add
possibilities. It is possible to speed up calculations by using probability trees. The app's capacity
to multiply and divide numbers will be appreciated by both children and their parents.
Ans 2.
Introduction
There are a few considerations to bear in mind if you want to obtain the most value for your money.
The temperature of the surrounding area should also be taken into account. It is feasible to modify
the dependent and independent variables to produce correlations and other properties of an
observation. Many issues may arise from poor handling of root (also known as base) variables.

As a result, the study's unique characteristics may be significantly influenced by this variable In
this case, logic and influence must be evaluated separately because of the speed at which they
affect the dependent variables and the possible direct impact they may have on them. In light of
the data, it may be difficult to distinguish between independent and dependent factors. People are
unable to discern one from the other, even when given the chance. The data may be changed if
there are non-researcher-related components to it.
In order to get more exact results, it is necessary to employ a variable to distinguish between
various properties of separate values. When it comes to aspects like these, temperature and peak
speed are two examples. Research has demonstrated that researchers prefer to concentrate on the
most relevant aspects of both observations when searching for correlations. The word "snarl" is
often used to describe the problem of lengthy travel times.
A product's pricing may be modified by the findings of an inquiry. Independent variables have no
effect on the experiment's results and do not impact each other. In the event that this occurs, the
model's independent variables are updated immediately.
The results of an experiment may be influenced by unrelated factors. This indicates that we expect
a significant contribution from you. The term "independent variables" refers to variables that are
not included in the dataset as a whole. Because the dependent variables were unaffected by other
factors, it had no effect on them. Independent variables may benefit from the inclusion of
explanatory factors since they provide light on the events that led to them. One way of determining
if a dependent variable influences research outcomes is by looking at independent factors.
Statistical analysis might be useful in this situation.

The diametric correlation between independent and dependent variables may be interpreted in a
variety of ways, depending on the context. Changing one or more of the situation's independent
variables, for example, might lead to a completely different course of action.. The term "response
variable" is used to describe the outcome of a successful transaction that involves one or more of
the many variables in question. Most important is how people perceive your conduct and attitudes
toward them. Each time the independent factors change, the dependent variables must likewise
change as a consequence. An independent variable's effect on a dependent variable may be
estimated using this kind of data. It is feasible to acquire an individual's idea of the transaction's
scale by using the simplest method available.
To make it more difficult to discern between components that are independent and those that are
dependent, a linear model is often used when there are many variables to be considered. The kinds
of questions that are asked in academic papers and comprehensive tests are in direct opposition to
each other. Analyze each of the components separately to determine whether the researcher's
perception of the situation is affected by any of them.
The regression equation bureaucracy to be,
.

P values, which are also known as association coefficients, are a typical approach to measure how
closely two variables are linked in a regression model. To represent the strength of a relationship
between two variables, we use the letter P. Statistical significance develops when the model and
the actual world are interwoven. It serves as an augmentation in this instance. Depending on the
context, the diametric correlation between independent and dependent variables may be interpreted
in a number of different ways. Altering the situation's independent factors, for example, can result
in a different course of action. A "response variable" characterises the outcome of a successful
transaction, which takes into account a wide range of variables. Behaviour and feelings toward
others are of the highest significance to others. As the independent factors change, so must the
dependent variables. Using this information, one may determine the effect of one independent
variable on another. It is possible to get an idea of how big a deal is by employing the most basic
method.
As numerous variables are involved, a linear model is often used to make it more difficult to
discern between independent and dependent components. The kind of questions asked in academic
papers vs comprehensive tests are poles apart. Examine each component one by one to see whether
it influences the researcher's perception of the situation.
In the original model's bureaucracy, the regression equations. When two variables have a
statistically significant connection, they are said to be in agreement. A P value indicates whether
or not a connection or relationship is statistically significant, and hence its relevance and
significance in the research in which it was discovered. It is important to verify that the projected
values are accurate using residual plots produced by a regression model after validation. You must
be able to analyse the data you've acquired after you've completed your estimations. Many studies
have found success in using linear regression to get the data they require for their investigations.
Conclusion

Researcher's work is only as fruitful as they can regulate how many independent variables are
amplifications when they are added. This is known to be an independent variable in scientific
circles, and we have precisely that here. In this case, additional factors will have no effect on the
dependent variables. To achieve the best accurate results, you should avoid utilising variables that
are peculiar to your business. It is more likely to effect the other variables if one is changed than
the other. The most common kind of "reaction variable" in fact analysis is the "reaction variable".
Respondent variables, on the other hand, may take on a broad variety of shapes and sizes.
Ans 3a.
Introduction
The Reels software has included video clips of less than 15 seconds. In addition to reels and
reminiscences, Instagram's IGTV is catching consumers' interest. When these tools are at your
fingertips, there are many opportunities to expand your Instagram following.
Concept and Application:
This is a new feature for the first time on Instagram: Instagram reels. Customers have used it during
typhoons. Within the application, consumers may now upload 15-second movies using Reels.
There are still many users who prefer the new services that don't immediately connect to video
sharing, even if Instagram TV and Stories have been there for a while and are well-known to many.
If you use these methods to promote your Instagram photographs and videos, you may see an
increase in their visibility. We must take use of this chance, but it doesn't need the participation of
everyone. To ensure that prospective customers are properly targeted, it is vital to validate present
customers and explore new markets. It takes a lot of time and money to put on a concert. You must
have this in mind and in your heart at all times. Despite their best efforts, many registrants are
unable to afford the registration fees.
Many people use the term "early adopters" to refer to those who embraced new technologies before
the mainstream. Those that embrace reels early will be rewarded, and those who do so will reap
the greatest rewards. There are just a few fundamental differences between Facebook and other
social media networks. Facebook places a high value on user feedback while developing new

features. Users argue that the inclusion of reels drew Indian viewers into the production process,
and that they were more interested in what was going on. A majority of Instagram users in India
(75 percent) utilise reels to attain the same end objective.
For 15 people out of 25 to love Instagram reels, the probability stands at,
N = 25
P = 0.75
Q= 0.25
x = 15, 20
Probability that Exactly 15 of them would agree with the claim
Px = NCx * P^x * Q^(N-x)
P(15) = 25C15 * (0.75)^15 * (0.25)^10
= 3268760 * 0.01336 * 0.00000095
= 0.0416
Probability that Exactly 20 of them would agree with the claim
Px = NCx * P^x * Q^(N-x)
P(20) = 25C20 * (0.75)^20 * (0.25)^5
= 53130 * 0.00317 * 0.000977
= 0.1645
Conclusion
If a user's target market falls inside the right demographic, they must try their luck and reach out
to a wider audience. Putting on a show requires a large investment of both time and money.
Fashionable clothing may be within the reach of certain individuals, particularly those who are
really invested in their work, but this is not always the case.

Ans 3b.
Introduction
Unprecedented efforts have been made to strengthen the hotel industry's infrastructure as a result
of recent technological and social developments. The hotel industry has evolved into one of the
world's most important, allowing countries to soar to previously inconceivable heights of
prosperity. Currently, Bharatdarshan is providing its customers with recordings of locations they
want to visit in the future.
Studying about our world's history should be done by those who spend most of their time at home.
When comparing and evaluating transportation alternatives, it is essential to take into consideration
the fluctuating nature of schedules and routes on public transit.
Passenger transportation will benefit from increased efficiency due to time travel. The story is far
from over, but this doesn't imply it in the traditional sense. Self-driving automobiles have the
potential to have profound effects on the environment and human society if they are successfully
adopted. Priority must be given to the most essential aspects of daily life if transportation
infrastructure is to be further developed. We hope you all have a safe and enjoyable ride to and
from your car this weekend.
This must be the ultimate goal of the operation, and it must be achieved as rapidly as possible for
it to be regarded a success. In the previous several decades, there have been many technological
and scientific advancements in the hotel industry. Several of the world's wealthiest countries have
seen an increase in their national economies due to the rise of the hotel industry.
Many individuals are unable to take a lengthy vacation now because of the high cost of living. It's
possible that you won't be able to go because of a lack of funds or other unforeseen situations. In
many cases, digital travel advocates' primary goal is to help their customers save money while on
vacation. Bharatdarshan is a great illustration of this. Depending on the service, consumers may
be able to watch video samples of locations they'd want to visit in the future.
The probability for the organization to get more than 12000 hits lies at,

P= 0.91
The probability for the organization to get fewer hits than 9000 lies at,
P= 1-(9000/10000)
= 0.1
Conclusion
For a variety of reasons, many people are unable to take a lengthy vacation or holiday. Some folks
may not be able to take their pets on vacation because of a lack of funds. As a result of this effort,
virtual travel has become more accessible to a broader range of people. We may learn much from
Bharat Darshan in this industry's best-known firm.

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