The document discusses probability terminology and examples. It defines key concepts like sample space, events, and probability functions. It provides examples of experiments like coin tosses and card deals. It also gives practice problems and questions about probability, events, and computing probabilities.
JEE Mathematics / Lakshmikanta Satapathy / Questions and Answers on Probability involving Independent events, mutually exclusive events in experiments of drawing colored balls from bags and problem solving probability of students using Addition theorem and Multiplication theorem
JEE Mathematics / Lakshmikanta Satapathy / Questions and Answers on Probability involving Independent events, mutually exclusive events in experiments of drawing colored balls from bags and problem solving probability of students using Addition theorem and Multiplication theorem
PROBABILITY FOR MIDDLE SCHOOL
Topics :
• The probability that an outcome does not happen
• Equally likely outcomes
• Listing all possible outcomes
• Experimental and theoretical probabilities
//&//
Community Nursing Research Strategy Masterclass
13th September 2013
The WSPCR was requested to organise a research masterclass for the Directors of Nursing from all the Welsh Health Boards on Friday 11th Sept. It was funded by the Health Minister and attended by the CNO. It also included the Head of the NISCHR and the manager of AHSC. The masterclass included the presentation of the Welsh Community Nurse Research Strategy which aims to raise the quality and quantity of research in Community Nursing in Wales. The workshop also generated further areas for research activity/priority.
http://www.wspcr.ac.uk/crns-masterclass-sep-2013.php
PROBABILITY FOR MIDDLE SCHOOL
Topics :
• The probability that an outcome does not happen
• Equally likely outcomes
• Listing all possible outcomes
• Experimental and theoretical probabilities
//&//
Community Nursing Research Strategy Masterclass
13th September 2013
The WSPCR was requested to organise a research masterclass for the Directors of Nursing from all the Welsh Health Boards on Friday 11th Sept. It was funded by the Health Minister and attended by the CNO. It also included the Head of the NISCHR and the manager of AHSC. The masterclass included the presentation of the Welsh Community Nurse Research Strategy which aims to raise the quality and quantity of research in Community Nursing in Wales. The workshop also generated further areas for research activity/priority.
http://www.wspcr.ac.uk/crns-masterclass-sep-2013.php
I am Christopher, T.I am a Mathematics Assignment Expert at eduassignmenthelp.com. I hold a PhD. in Mathematics, University of Alberta, Canada. I have been helping students with their Assignments for the past 7 years. I solve assignments related to Mathematics.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com . You can also call on +1 678 648 4277 for any assistance with Mathematics Assignments.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 2 Solutions
Chapter 4: Probability
I am Josh U. I am a Probability Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from St. Edward’s University, USA.
I have been helping students with their homework for the past 5 years. I solve assignments related to Probability. Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Probability Assignments.
Some Basic concepts of Probability along with advanced concepts on Medical probability & Probability in Gambling. A lot of Sample Questions and Practice Questions will help you understand and apply the concepts in real life.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
3. Board Question
Deck of 52 cards
13 ranks: 2, 3, . . . , 9, 10, J, Q, K, A
4 suits: ♥, ♠, ♦, ♣,
Poker hands
Consists of 5 cards
A one-pair hand consists of two cards having one rank and the
remaining three cards having three other rank
Example: {2♥, 2♠, 5♥, 8♣, K♦}
Question
a) How many different 5 card hands have exactly one pair?
Hint: practice with how many 2 card hands have exactly one pair.
Hint for hint: use the rule of product.
b) What is the probability of getting a one pair poker hand?
April 22, 2014 3 / 22
4. Clicker Test
Set your clicker channel to 41.
Do you have your clicker with you?
No = 0
Yes = 1
April 22, 2014 4 / 22
5. Probability Cast
Introduced so far
Experiment: a repeatable procedure
Sample space: set of all possible outcomes S (or Ω).
Event: a subset of the sample space.
Probability function, P(ω): gives the probability for
each outcome ω ∈ S
1. Probability is between 0 and 1
2. Total probability of all possible outcomes is 1.
April 22, 2014 5 / 22
6. Example (from the reading)
Experiment: toss a fair coin, report heads or tails.
Sample space: Ω = {H, T}.
Probability function: P(H) = .5, P(T) = .5.
Use tables:
Outcomes H T
Probability
1/2 1/2
(Tables can really help in complicated examples)
April 22, 2014 6 / 22
8. Events
Events are sets:
Can describe in words
Can describe in notation
Can describe with Venn diagrams
Experiment: toss a coin 3 times.
Event:
You get 2 or more heads = { HHH, HHT, HTH, THH}
April 22, 2014 8 / 22
9. CQ: Events, sets and words
Experiment: toss a coin 3 times.
Which of following equals the event “exactly two heads”?
A = {THH, HTH, HHT, HHH}
B = {THH, HTH, HHT}
C = {HTH, THH}
(1) A (2) B (3) C (4) A or B
April 22, 2014 9 / 22
10. CQ: Events, sets and words
Experiment: toss a coin 3 times.
Which of the following describes the event
{THH, HTH, HHT}?
(1) “exactly one head”
(2) “exactly one tail”
(3) “at most one tail”
(4) none of the above
April 22, 2014 10 / 22
11. CQ: Events, sets and words
Experiment: toss a coin 3 times.
The events “exactly 2 heads” and “exactly 2 tails” are
disjoint.
(1) True (2) False
April 22, 2014 11 / 22
12. CQ: Events, sets and words
Experiment: toss a coin 3 times.
The event “at least 2 heads” implies the event “exactly
two heads”.
(1) True (2) False
April 22, 2014 12 / 22
13. Probability rules in mathematical notation
Sample space: S = {ω1, ω2, . . . , ωn}
Outcome: ω ∈ S
Probability between 0 and 1:
Total probability is 1:
Event A: P(A)
April 22, 2014 13 / 22
14. Probability and set operations on events
Rule 1. Complements. .
Rule 2. Disjoint events.
Rule 3. Inclusion-exclusion principle.
A
Ac
Ω = A ∪ Ac
, no overlap
L R
L ∪ R, no overlap
L R
L ∪ R, overlap = L ∩ R
April 22, 2014 14 / 22
15. Concept question
Class has 50 students
20 male (M), 25 brown-eyed (B)
For a randomly chosen student what is the range of
possible values for p = P(M ∪ B)?
(a) p ≤ .4
(b) .4 ≤ p ≤ .5
(c) .4 ≤ p ≤ .9
(d) .5 ≤ p ≤ .9
(e) .5 ≤ p
April 22, 2014 15 / 22
16. Table Question
Experiment:
1) Roll your 20-sided die.
2) Check if all rolls at your table are distinct.
Repeat the experiment five times and record the results.
April 22, 2014 16 / 22
17. Table Question
Experiment:
1) Roll your 20-sided die.
2) Check if all rolls at your table are distinct.
Repeat the experiment five times and record the results.
For this experiment, how would you define the sample
space, probability function, and event?
Compute the exact probability that all rolls are distinct.
April 22, 2014 16 / 22
18. Concept Question
Lucky Larry has a coin that you’re quite sure is not fair.
He will flip the coin twice
It’s your job to bet whether the outcomes will be the
same (HH, TT) or different (HT, TH).
Which should you choose?
1. Same
2. Different
3. It doesn’t matter, same and different are equally likely
April 22, 2014 17 / 22
19. Board Question
Lucky Larry has a coin that you’re quite sure is not fair.
He will flip the coin twice
It’s your job to bet whether the outcomes will be the
same (HH, TT) or different (HT, TH).
Which should you choose?
1. Same 2. Different 3. Doesn’t matter
Question: Let p be the probability of heads and use
probability to answer the question.
(If you don’t see the symbolic algebra try p = .2, p=.5)
April 22, 2014 18 / 22
20. Jon’s dice
Jon has three six-sided dice with unusual numbering.
A game consists of two players each choosing a die. They
roll once and the highest number wins.
Which die would you choose?
April 22, 2014 19 / 22
21. Board Question
Compute the exact probability of red beating white.
1) For red and white dice make the probability table.
2) Make a prob. table for the product sample space of red
and white.
3) What is the probability that red beats white?
April 22, 2014 20 / 22
22. Answer to board question
For each die we have a probability table
Red die White die
Outcomes 3 6 Outcomes 2 5
Probability 5/6 1/6 Probability 1/2 1/2
For both together we get a 2 × 2 probability table
White
2 5
Red 3 5/12 5/12
6 1/12 1/12
The red table entries are those where red beats white. Totalling the
probability we get P(red beats white) = 7/12.
April 22, 2014 21 / 22
23. Concept Question
We saw red is better than white.
We’ll tell you that white is better than green.
So red is better than white is better than green.
Is red better than green?
April 22, 2014 22 / 22