The document provides an introduction to probability concepts including sample space, events, simple and compound events, calculating probabilities as fractions or decimals, certain, impossible, and complementary events. It gives examples of determining the sample space and probabilities for experiments involving rolling dice, flipping coins, and drawing cards. It poses questions about identifying sample spaces and calculating probabilities for experiments combining dice rolls, coin flips, and bus and train arrival times.
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.
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
Hello our respected institutions and faculties
if you want to buy Editable materials (6 to 12th/Foundation/JEE/NEET/CET) for your institution
Contact me ... 8879919898
*CBSE 6 TO 10 TOPICWISE PER CHAPTER 100 QUESTION WITH ANSWER MATHEMATICS & SCIENCE & SST (Biology,Physics,Chemistry & Social studies)* Editable ms word
# *Neet/JEE(MAINS) PCMB*
# *IIT ( advance) PCM*
# *CET (PCMB) level with Details solutions*
(All jee,neet,advance,cet mcq's Count 1 lakh 50k ) data of all subjects*
*TOPICWISE WISE DPP PCMB NEW PATTERN AVILABLE*
Or also study material for *neet and jee* and *foundation* new Material with solutions
Like
*👉🏽Foundation( Class 6th to 10th) Editable Material Latest Available 👇..*
1. VMC - All Subjects
2. Carrer Point(Kota) - All Subjects
3. Bansal Classes - All Subjects
4. Narayana - All Subjects
5. Mentors - All Subjects
6. Brilliants - All Subjects
7. Resonance - All Subjects
8. Motioniitjee - All Subjects
9. Rao(Kota) - All Subjects
10. Insight - All Subjects
11. Allen - All Subjects
12. FITJEE - All Subjects
13. Abhyas Gurukul - All Subject
14. Parth Ashram - All Subject
Many Other+++
*👉🏽All IIT-JEE & NEET Coachings Editable 📚Study Material Latest Available..👇🏼*
1. Narayana - PCMB
2. Etoos India - PCMB
3. Brilliant- PCM
4.Career Point(Kota) - PCMB
5. Bansal - PCMB
6. Resonance - PCMB
7. Sri Chaitanya - PCM
8. Aakash(Delhi) - PCMB
9. Fitjee - PCM
10. Mastermind - PCMB
11. Mentors - PCB
12. Allen - PCMB
13. Plancess - PCMB
14. VMC - PCM
15. Motioniitjee - PCM
16. Nishith - PCM
17. Arride (Kota) - PCM
18. Rao IIT Acad. - PCM
19. Pulse - PCB
20. Abhyas Gurukul - PCMB
21. Drona - PCMB
22. Active Site - PCMB
23. Vision - PCM
24. Parth Ashram - PCMB
25. Brainsmiths - PCM
26. Infinite - PCM
27. Ekalavya - PCM
28. Trick Based - PCM
...
& Many Other Institute Complete Material Available ++.. Also Editable Books 📚 Available
⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️
👉 *Teaching Notes & PPTs (PCMB Editable) are Available in colourful*
**New material Exchange offer also available **
*Those who want Pls contact us...*
or also have {All Etoos, Akash(i-tutor) Digital, Allen, NeetPrep Digital, neuclion, Neuclius Education ,Plancess, SSC, Airforce, CAT, GATE IIT-JAM, NIMCET, IAS pre + mains (RAS Pre + Mains), UPTET,CTET,STET, vedio lacture *(also KG TO 12th Animated video Lecture Language English & Hindi)*} contact with us........👇
For Sample Massage me .
Behind Their Eyes - making thinking visible is not enough
Walk into any classroom and watch the breakneck pace at which teachers are working hard to help students learn. Mind you, if we don’t uncover what students are thinking while learning, they may be running down the wrong path. OK, so we need ways to make student thinking visible. Seeing their thinking is important, but we also need to create the time and space for teachers to absorb, reflect, and act on what their students thinking reveals. This workshop shares strategies both for making student thinking visible and for creating time and space for teachers to meaningfully act on what they learn about what’s going on behind their eyes.
“If you really want to understand something, try changing it.” - Kurt Lewin
As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
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.
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
Hello our respected institutions and faculties
if you want to buy Editable materials (6 to 12th/Foundation/JEE/NEET/CET) for your institution
Contact me ... 8879919898
*CBSE 6 TO 10 TOPICWISE PER CHAPTER 100 QUESTION WITH ANSWER MATHEMATICS & SCIENCE & SST (Biology,Physics,Chemistry & Social studies)* Editable ms word
# *Neet/JEE(MAINS) PCMB*
# *IIT ( advance) PCM*
# *CET (PCMB) level with Details solutions*
(All jee,neet,advance,cet mcq's Count 1 lakh 50k ) data of all subjects*
*TOPICWISE WISE DPP PCMB NEW PATTERN AVILABLE*
Or also study material for *neet and jee* and *foundation* new Material with solutions
Like
*👉🏽Foundation( Class 6th to 10th) Editable Material Latest Available 👇..*
1. VMC - All Subjects
2. Carrer Point(Kota) - All Subjects
3. Bansal Classes - All Subjects
4. Narayana - All Subjects
5. Mentors - All Subjects
6. Brilliants - All Subjects
7. Resonance - All Subjects
8. Motioniitjee - All Subjects
9. Rao(Kota) - All Subjects
10. Insight - All Subjects
11. Allen - All Subjects
12. FITJEE - All Subjects
13. Abhyas Gurukul - All Subject
14. Parth Ashram - All Subject
Many Other+++
*👉🏽All IIT-JEE & NEET Coachings Editable 📚Study Material Latest Available..👇🏼*
1. Narayana - PCMB
2. Etoos India - PCMB
3. Brilliant- PCM
4.Career Point(Kota) - PCMB
5. Bansal - PCMB
6. Resonance - PCMB
7. Sri Chaitanya - PCM
8. Aakash(Delhi) - PCMB
9. Fitjee - PCM
10. Mastermind - PCMB
11. Mentors - PCB
12. Allen - PCMB
13. Plancess - PCMB
14. VMC - PCM
15. Motioniitjee - PCM
16. Nishith - PCM
17. Arride (Kota) - PCM
18. Rao IIT Acad. - PCM
19. Pulse - PCB
20. Abhyas Gurukul - PCMB
21. Drona - PCMB
22. Active Site - PCMB
23. Vision - PCM
24. Parth Ashram - PCMB
25. Brainsmiths - PCM
26. Infinite - PCM
27. Ekalavya - PCM
28. Trick Based - PCM
...
& Many Other Institute Complete Material Available ++.. Also Editable Books 📚 Available
⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️
👉 *Teaching Notes & PPTs (PCMB Editable) are Available in colourful*
**New material Exchange offer also available **
*Those who want Pls contact us...*
or also have {All Etoos, Akash(i-tutor) Digital, Allen, NeetPrep Digital, neuclion, Neuclius Education ,Plancess, SSC, Airforce, CAT, GATE IIT-JAM, NIMCET, IAS pre + mains (RAS Pre + Mains), UPTET,CTET,STET, vedio lacture *(also KG TO 12th Animated video Lecture Language English & Hindi)*} contact with us........👇
For Sample Massage me .
Behind Their Eyes - making thinking visible is not enough
Walk into any classroom and watch the breakneck pace at which teachers are working hard to help students learn. Mind you, if we don’t uncover what students are thinking while learning, they may be running down the wrong path. OK, so we need ways to make student thinking visible. Seeing their thinking is important, but we also need to create the time and space for teachers to absorb, reflect, and act on what their students thinking reveals. This workshop shares strategies both for making student thinking visible and for creating time and space for teachers to meaningfully act on what they learn about what’s going on behind their eyes.
“If you really want to understand something, try changing it.” - Kurt Lewin
As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore inquiry as a pedagogical stance and the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants will leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
This participatory session will engage attendees in some meaningful dialogue around several aspects of digital citizenship. We'll explore some hot-button topics and consider their impact on the work we do as educators. This session will provide clarification around a number of key digital citizenship issues and will also highlight a valuable model for engaging your students in classroom conversations. There’s a fair bit of fear mongering disguised as digital citizenship online. Our kids need more models of empathy and empowerment – so do we. We’ll share some of those models too.
Presented at the Riding the Wave Conference in Gimli, Manitoba. May 2017.
In two words, you remember the whole story: glass slipper, sour grapes, cold porridge. You remember more than facts, you recall relationships & deeper connections between characters. Some of the powerful ways we leverage digital for deeper learning includes challenging sources of information (fake news), exploring bias (developing empathy through multiple perspectives), and creating powerful feedback loops that foster deeper learning.
Powerful narratives, in a word or two, bring to mind a wealth of ideas & relationships; more than just facts. How can we find stories that make our teaching sticky and help kids find, and more importantly tell, stories that make learning stick? This workshop will equip teachers with the skills & knowledge to foster deeper learning across the curriculum by intentionally leveraging digital tools to foster deeper learning.
Tales of Learning and the Gifts of Footprints v4.2Darren Kuropatwa
Presented at the Richmond District Conference, Feb 2017.
Why does digital learning matter? In a society that is increasingly technophilic what are the new literacies we need to be aware of for our own learning and that of our students? How does this impact the way we think about and teach our children to become empowered and empathetic responsible citizens? Answers to these questions and more are shared through a series of powerful tales of learning.
Presented at the Richmond District Conference, Feb 2017.
A series of stories woven together to start a conversation with middle and high school students, teachers, and parents about living our lives on and offline (on The Fourth Screen) more thoughtfully.
This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning. Held at the BYTE Conference 2017 in Portage la Prairie, Manitoba.
A group of educators from the BYTE Conference 2017 (Build Your Teaching Experience) share their ideas about learning as a series of visual metaphors they found on their phones.
Slides to support a master class at the PRIZMAH Conference in Chicago, IL. 5 Feb 2017.
How can we make learning sticky using powerful storytelling frameworks that tap into peoples' emotions? How do we involve all students in creating digital content that doesn't also create hours of content for teachers to assess? This interactive session will showcase Digital Storytelling activities teachers can use in class tomorrow! Document student learning & foster reflective ways for students to share their learning. 1st: we play! Then we'll discuss how to practically adapt these ideas, make them your own, and figure out what sort of infrastructure needs to be in place to support these kinds of powerful learning experiences. We’ll learn how to exercise your students' & your own creativity muscles and share simple strategies for collecting & publishing student work.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
A series of stories woven together to start a conversation with middle and high school students about living our lives on and offline (on The Fourth Screen) more thoughtfully.
This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning.
A group of educators from the Anderson Union High School & Redding School Districts and share their ideas about learning as a series of visual metaphors.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
A series of stories woven together to start a conversation with middle and high school students about living our lives on and offline (on The Fourth Screen) more thoughtfully.
This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
Slides to support a master class at the Building Learning Communities Conference in Boston, MA. 18 July 2016.
How can we make learning sticky using powerful storytelling frameworks that tap into peoples' emotions? How do we involve all students in creating digital content that doesn't also create hours of content for teachers to assess? This interactive session will showcase Digital Storytelling activities teachers can use in class tomorrow! Document student learning & foster reflective ways for students to share their learning. 1st: we play! Then we'll discuss how to practically adapt these ideas, make them your own, and figure out what sort of infrastructure needs to be in place to support these kinds of powerful learning experiences. We’ll learn how to exercise your students' & your own creativity muscles and share simple strategies for collecting & publishing student work.
Slides in support of a professional learning day for administrators in Hanover School Division focused on developing a common language & understanding of Deep Learning Design.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
Generating a custom Ruby SDK for your web service or Rails API using Smithyg2nightmarescribd
Have you ever wanted a Ruby client API to communicate with your web service? Smithy is a protocol-agnostic language for defining services and SDKs. Smithy Ruby is an implementation of Smithy that generates a Ruby SDK using a Smithy model. In this talk, we will explore Smithy and Smithy Ruby to learn how to generate custom feature-rich SDKs that can communicate with any web service, such as a Rails JSON API.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...
Pre-Cal 40S Slides May 21, 2008
1. What is the probability that the sky will fall?
Write your answer as a fraction.
Do not discuss with a neighbour.
An Introduction to Probability
http://mathforum.org/dr.math/faq/faq.prob.intro.html
Chicken Little by flickr user damonj74
2.
3. Some vocabulary ...
Probability: the branch of mathematics that deals with chance.
Sample Space (Ω): the set of all possible outcomes for a given
quot;Experimentquot; represented by capital omega Ω.
Event (E): A subset of the sample space. A particular occurance
in a given experiment.
Simple Event: The result of an experiment that is carried out in
a single step.
Example: Flip a coin. The result is heads
(a simple event)
Compound Event: The result of an experiment carried out in two
(or more) steps.
Example 1: Flip a coin and roll a die - 6 .The result is {H,6}
Example 2: Flip a coin twice. The result is {H,T}
4. Calculating the Probability of Event A
number of favourable
outcomes
sample space
Probability can be expressed as:
- a Ratio
- a Fraction IMPORTANT: Probability of any event
- a Decimal is always a number between 0 and 1.
- a Percent
5. Certain Event: an event whose probability is 1
Example: roll a die - 6 and get a result less than 10
Impossible Event: an event whose probability is 0.
Example: roll a die - 6 and get a 7
Complimentary Event: the compliment of E is E':
If P(E) = a then P(E') = 1-a
Example: Given a standard deck of cards, a card is drawn at
random.
P(spade) = (13/52) = (1/4)
P (not a spade) = 1 - (1/4) = (3/4)
6. Determine the sample space when a fair die is rolled once.
Solution: It is possible to roll a 1, 2, 3, 4, 5 or 6.
This is the sample space. {1, 2, 3, 4, 5, 6}
Determine the sample space for rolling a six sided die and flipping
a coin.
7. Determine the probability of rolling a 2 when rolling a fair die.
Determine the probability of getting a head and an odd number
when rolling a die and flipping a coin.
8. A coin is flipped three times. Draw a tree diagram to illustrate the
sample space.
9. A fair six-sided die is rolled twice. Draw a chart to illustrate the
sample space.
10. A bus is scheduled to arrive at a train station at any time between 07:05
and 07:15 inclusive. A train is scheduled to arrive between 07:11 and
07:17 inclusive. The arrival of a bus at 7:06 and a train at 07:14 can be
represented by the ordered pair (6, 14). Times are expressed in whole
minutes.
a) Sketch a sample space for this event (use a chart).
b) How many ordered pairs are there in this sample space?
c) How many ordered pairs have the bus and the train arriving
at the same time?
d) How many ordered pairs have the train arriving after the bus?
e) What is the probability of the bus arriving after the train?