Applied Math 40S February 25, 2008
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The document discusses experimental and theoretical probability. It provides an example of calculating the theoretical probability of having 2 girls in a family with 3 children. The theoretical probability is calculated as 1/4 or 25% since there are 4 possible combinations (BBB, BBG, GBB, BGG) and only 1 of those combinations results in 2 girls.
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Slides February 23rd
The document discusses experimental and theoretical probability. Experimental probability is determined by repeated testing and observing results, calculated as the number of times an event occurred divided by the total number of tests. Theoretical probability is calculated under ideal circumstances based on possible outcomes. For a family with 3 children, the theoretical probability of having 2 girls can be calculated as the number of ways to have 2 girls (3 combinations) divided by the total possible outcomes (8 combinations). An example is also given of simulating a binomial experiment using a calculator to determine the probability of getting exactly 2 heads when flipping 3 coins 40 times.
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This document discusses binomial experiments and probability. It provides instructions on how to simulate binomial experiments using a TI-83 calculator or the Random.org website. It includes examples of using coins to simulate a true/false test and a multiple choice test. It also mentions Pascal's triangle and different patterns that can be found within it.
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Theoretical probability is calculated based on all possible outcomes, while experimental probability is calculated based on observed outcomes from an experiment. The document provides examples of calculating theoretical and experimental probabilities from sample spaces involving marbles drawn from a bag, student juice preferences in a class, movie preferences in surveys, and dice rolls. Probabilities are provided as fractions of possible outcomes.
Lecture: Experimental and Theoretical Probability
This document discusses theoretical and experimental probability. Theoretical probability is calculated based on known information about possible outcomes, like flipping a coin. Experimental probability is based on data collected from experiments. Theoretical probability predicts outcomes, while experimental probability shows observed frequencies. Examples show calculating probabilities from rolling a die and spinning a spinner. Probabilities can be expressed as fractions, decimals, or percentages.
Experimental probability pp
The document discusses experimental probability and how it is calculated by performing trials of an experiment and recording the number of successful outcomes. It provides examples of calculating experimental probability based on rolling dice and cars moving in a race based on dice rolls. The document aims to help students understand what experimental probability means, become familiar with experimenting with chance, and compare experimental and actual probability.
Experimental prob grand_demo_ppt2 (2)
Here are 3 experiments with their experimental probabilities:
1. Flipping a coin 10 times and recording heads or tails. I got 6 heads.
The experimental probability of getting heads on the next flip is 6/10 or 60%
2. Drawing marbles from a bag containing 5 red and 3 blue marbles. I drew 4 red marbles.
The experimental probability of drawing a red marble on the next draw is 4/8 or 50%
3. Rolling a die and recording the results. I rolled a 3, 5, 2, 4, 1, 6.
The experimental probability of rolling a 5 on the next roll is 1/6 or 16.67%
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This document discusses probability and simple events. It begins with examples of rolling dice and finding the probabilities of various outcomes. It then defines key probability terms like sample space, complementary events, and the range of probabilities from 0 to 1. Several probability calculation examples are given for dice rolls, card draws, and spinners. The document emphasizes that the probability of an event is a number between 0 and 1, and discusses how to calculate probabilities and complementary events.
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Slides February 23rd
The document discusses experimental and theoretical probability. Experimental probability is determined by repeated testing and observing results, calculated as the number of times an event occurred divided by the total number of tests. Theoretical probability is calculated under ideal circumstances based on possible outcomes. For a family with 3 children, the theoretical probability of having 2 girls can be calculated as the number of ways to have 2 girls (3 combinations) divided by the total possible outcomes (8 combinations). An example is also given of simulating a binomial experiment using a calculator to determine the probability of getting exactly 2 heads when flipping 3 coins 40 times.
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Review: experimental vrs. theoretical probability, designing simulations, using the randBin() command on the TI-83, calculating theoretical probabilities using "and" and "or".
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Experimental probability pp
The document discusses experimental probability and how it is calculated by performing trials of an experiment and recording the number of successful outcomes. It provides examples of calculating experimental probability based on rolling dice and cars moving in a race based on dice rolls. The document aims to help students understand what experimental probability means, become familiar with experimenting with chance, and compare experimental and actual probability.
Experimental prob grand_demo_ppt2 (2)
Here are 3 experiments with their experimental probabilities:
1. Flipping a coin 10 times and recording heads or tails. I got 6 heads.
The experimental probability of getting heads on the next flip is 6/10 or 60%
2. Drawing marbles from a bag containing 5 red and 3 blue marbles. I drew 4 red marbles.
The experimental probability of drawing a red marble on the next draw is 4/8 or 50%
3. Rolling a die and recording the results. I rolled a 3, 5, 2, 4, 1, 6.
The experimental probability of rolling a 5 on the next roll is 1/6 or 16.67%
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This document discusses probability and simple events. It begins with examples of rolling dice and finding the probabilities of various outcomes. It then defines key probability terms like sample space, complementary events, and the range of probabilities from 0 to 1. Several probability calculation examples are given for dice rolls, card draws, and spinners. The document emphasizes that the probability of an event is a number between 0 and 1, and discusses how to calculate probabilities and complementary events.
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This document contains lesson material on probability, including vocabulary definitions and examples. It defines key terms like probability, sample space, theoretical probability, and experimental probability. It provides examples of calculating probabilities of events occurring based on the number of possible outcomes. For instance, the probability of randomly selecting a green marker from three colors is 1/3, and the probability of guessing someone's birthday within 31 days is 1/31. The document also distinguishes between theoretical and experimental probability and provides examples of calculating each.
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The document discusses theoretical and experimental probability. It provides examples of calculating probabilities from rolling dice or drawing marbles from a bag. It explains that theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Experimental probability is calculated based on observed outcomes from experiments. The document provides practice problems and solutions for students to calculate probabilities in different scenarios.
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(7) Lesson 9.2
The theoretical probability of rolling a sum of 10 when rolling two number cubes is 5/36.
There are 6 possible ways to roll a sum of 10: (1,9), (2,8), (3,7), (4,6), (5,5), (6,4).
There are 6 combinations that result in a sum of 10 out of the total possible combinations when rolling two number cubes, which is 6^2 = 36 possible outcomes.
Therefore, the theoretical probability is 5/36.
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2) Students will toss two coins 100 times in groups and record head/head, head/tail, and tail/tail outcomes. They will then use a chi-square test to compare observed results to expected results based on probability laws.
3) The chi-square test allows students to determine if any differences between observed and expected results are statistically significant, which could mean factors other than chance are influencing the outcomes. This analysis method is important for studying inheritance patterns in genetics.
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This document provides an overview of theoretical probability concepts including:
- Theoretical probability is calculated as the number of favorable outcomes divided by the total number of equally likely outcomes.
- Experiments are considered "fair" if all outcomes are equally likely.
- The probability of an event occurring plus the probability of it not occurring equals 1.
- Complement probability refers to outcomes not included in the main event.
- Odds can be used to express likelihood and converted to and from probabilities using ratios of favorable to total outcomes.
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The theoretical probability of rolling a sum of 10 when rolling two number cubes is 5/36.
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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.
Learning is at AUHSD
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.
Providing Permission to Wonder v2
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.
The Fourth Screen v4
This document contains a collection of images, quotes, and short passages on topics related to online communities, sharing, and empowerment through technology. The snippets discuss how the internet allows information to be easily shared, encourages learning, and can help empower victims of bullying. The overarching theme is about the positive impact community and connection through online platforms can provide.
Learning is at BLC16
A group of educators at the Building Learning Communities Conference share their ideas about learning as a series of visual metaphors.
We Learn Through Stories v4 (master class)
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.
Deep Learning Design: the middle ring
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.
More from Darren Kuropatwa (20)
Tales of Learning and the Gifts of Footprints v4.2
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Choosing The Best AWS Service For Your Website + API.pptx
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
Join me in this session as we dive into each AWS hosting service to determine which one is best for your scenario and explain why!
OpenID AuthZEN Interop Read Out - Authorization
During Identiverse 2024 and EIC 2024, members of the OpenID AuthZEN WG got together and demoed their authorization endpoints conforming to the AuthZEN API
Driving Business Innovation: Latest Generative AI Advancements & Success Story
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
During the hour, we’ll take you through:
Guest Speaker Segment with Hannah Barrington: Dive into the world of dynamic real estate marketing with Hannah, the Marketing Manager at Workspace Group. Hear firsthand how their team generates engaging descriptions for thousands of office units by integrating diverse data sources—from PDF floorplans to web pages—using FME transformers, like OpenAIVisionConnector and AnthropicVisionConnector. This use case will show you how GenAI can streamline content creation for marketing across the board.
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This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
Digital Marketing Trends in 2024 | Guide for Staying Ahead
https://www.wask.co/ebooks/digital-marketing-trends-in-2024
Feeling lost in the digital marketing whirlwind of 2024? Technology is changing, consumer habits are evolving, and staying ahead of the curve feels like a never-ending pursuit. This e-book is your compass. Dive into actionable insights to handle the complexities of modern marketing. From hyper-personalization to the power of user-generated content, learn how to build long-term relationships with your audience and unlock the secrets to success in the ever-shifting digital landscape.
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
UiPath Test Automation using UiPath Test Suite series, part 6
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
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Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
GraphRAG for Life Science to increase LLM accuracy
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5th LF Energy Power Grid Model Meet-up Slides
5th Power Grid Model Meet-up
It is with great pleasure that we extend to you an invitation to the 5th Power Grid Model Meet-up, scheduled for 6th June 2024. This event will adopt a hybrid format, allowing participants to join us either through an online Mircosoft Teams session or in person at TU/e located at Den Dolech 2, Eindhoven, Netherlands. The meet-up will be hosted by Eindhoven University of Technology (TU/e), a research university specializing in engineering science & technology.
Power Grid Model
The global energy transition is placing new and unprecedented demands on Distribution System Operators (DSOs). Alongside upgrades to grid capacity, processes such as digitization, capacity optimization, and congestion management are becoming vital for delivering reliable services.
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What to expect
For the upcoming meetup we are organizing, we have an exciting lineup of activities planned:
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The original Czech 🇨🇿 version of the presentation can be found here: https://www.slideshare.net/slideshow/hlavni-novinky-souvisejici-s-ccs-tsi-2023-2023-1695/269688092 .
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Overview
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Key Topics Covered
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4. Deployment Using ArgoCD for Edge Devices
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5. Introduction to Apache Kafka and S3
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7. What is Prometheus?
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8. Monitoring Application Metrics with Prometheus
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10. Configuring Camel K Integrations for Data Pipelines
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11. What is a Jupyter Notebook?
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Introduction of Cybersecurity with OSS at Code Europe 2024
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Generating privacy-protected synthetic data using Secludy and Milvus
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Fueling AI with Great Data with Airbyte Webinar
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Building Production Ready Search Pipelines with Spark and Milvus
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Choosing The Best AWS Service For Your Website + API.pptx
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
UiPath Test Automation using UiPath Test Suite series, part 6
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Programming Foundation Models with DSPy - Meetup Slides
Programming Foundation Models with DSPy - Meetup Slides
Introduction of Cybersecurity with OSS at Code Europe 2024
Introduction of Cybersecurity with OSS at Code Europe 2024
Generating privacy-protected synthetic data using Secludy and Milvus
Generating privacy-protected synthetic data using Secludy and Milvus
Building Production Ready Search Pipelines with Spark and Milvus
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Applied Math 40S February 25, 2008
- 1. Experimental and Theoretical Probability In a family of three children, what is the probability that 2 of the children will be girls? one two three
- 2. In a family of three children, what is the probability that 2 of the children will be girls? Experimental Probability: The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, to find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played.
- 3. In a family of three children, what is the probability that 2 of the children will be girls? Theoretical Probability: The chances of events happening as determined by calculating results that would occur under ideal circumstances. For example, the theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4, and under ideal circumstances one out of every four rolls would be a 4. Contrast this with experimental probability.
- 4. In a family of three children, what is the probability that 2 of the children will be girls? Theoretical Probability
- 5. Binomial Experiments & Probability DICTIONARY Simulating Binomial Experimets: randBin(# of trials, prob. of success, # of simulations) What is the probability of getting exactly 2 heads when fliping 3 coins 40 times? You'll need to know the the theoretical probability of this result is 3/8. Here is how to do the experiment on your calculator. Step Action 1. Press [Math] button on TI83 calculator. 2. Select [Prob]. 3. Select [randBin] (random binomial experiment). 4. Type in (1, 3/8, 40) . 1 represents the outcome for success (failure is 0). little predator 3/8 represents the theoretical probability of success. 40 represents number of times the experiment is repeated. 5. Press enter and a result will show in row. 6. Press [STO] [2nd] [L1] to store the results in List 1. 7. Press [2nd] [STAT]. 8. Select [MATH] [Sum] [2nd] [L1] to find the sum of all the values in List 1. 9. Since quot;success = 1quot; and quot;failure = 0quot; this sum represents the number of successes. You can also use this website: Random.org http://www.random.org/
- 6. HOMEWORK What is the probability of spinning each of the following using the spinner shown? The colours on the spinner are red, yellow, and blue. 1. P(red) 2. P(yellow) 3. P(green) 4. P(red, yellow or blue) 5. P(not red)
- 7. HOMEWORK Design an experiment using coins to simulate a 10 question true/false test. What is the experimental probability of scoring at least 70% on the test if you guess each answer?
- 8. HOMEWORK Design an experiment to determine the probability of passing a six-question multiple choice test if you guess all the answers. Each question has four answers, and one answer is correct in each case. How many simulations would seem reasonable? What is the experimental probability of getting at least 50% on the test?