Students extend their understanding of compound events. They will compare experimental results to predicted results by calculating the probability of an event, then conducting an experiment.Key ConceptsStudents apply their understanding of compound events to actual experiments.Students will see there is variability in actual results.Goals and Learning ObjectivesContinue to explore compound independent events.Compare theoretical probability to experimental probability.

Students begin learning about compound events by considering independent events. They will consider everyday objects with known probabilities. Students will represent sample spaces using lists, tables, and tree diagrams in order to calculate the probability of certain events.Key ConceptsCompound events are introduced in this lesson, building upon what students have learned about determining sample space and probabilities of single events.Terms introduced are:multistage experiment: an experiment in which more than one action is performedcompound events: the combined results of multistage experimentsindependent events: compound events in which the outcome of one does not affect the outcome of the otherGoals and Learning ObjectivesLearn about compound events and sample spaces.Use different tools to find the sample space (tree diagrams, tables, lists) of a compound event.Use ratio and proportion to solve problems.SWD: Go over the mathematical language used throughout the module. Make sure students use that language when discussing problems in this lesson.

Students will continue to apply their understanding of compound independent events. They will calculate probabilities and represent sample spaces with visual representations.Key ConceptsStudents continue to solve problems with compound events. The formula for calculating the probability of independent events is introduced:P(A and B) = P(A) ⋅ P(B)Goals and Learning ObjectivesDeepen understanding of compound events using lists, tables, and tree diagrams.Learn about the Fundamental Counting Principle.

Gallery OverviewAllow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.Chance of RainStudents are given the probability that it will rain on two different days and asked to find the chance that it will rain on one of the two days.PenguinsIn an Antarctic penguin colony, 200 penguins are tagged and released. A year later, 100 penguins are captured and 4 of them are tagged. Students determine how many penguins are in the colony.How Many Yellow?Given the total number of balls in a bag and the probability for two colors, students find the number of balls for the third color.How Many Ways to Line Up?Students decide how many different ways they five students can order themselves as they line up for class.Gumballs There are some white gumballs and red gumballs left in a machine. Students find the probability of getting at least one red gumball.New FamilyA married couple wants to have four children. Students find the probability that at least one child will be a girl.Nickel and DimeStudents find the probability for different outcomes when tossing two coins.Four More FlipsStudents determine how many more tails are likely if a coin has already landed on tails twice.Bubble GumThe letters G, U, or M are printed inside bubble gum wrappers in a ratio of 3:2:1. Students use a simulation to find out how much bubble gum to buy to get a 3:2:1 ratio.A Large FamilyIf a family wants to have six children, what is the probability that there will be three boys and three girls? Students use a simulation to model the probability.No TelephoneUsing census data from 1960 and 1990 in two box plots, students compare the percentages of families that had phones.Pulse RateStudents compare two data sets of different sizes: one for students and one for athletes.Golf ScoresStudents are given two sets of golf scores for Rosa and Chen. They are asked to decide who is the better golfer by constructing and comparing box plots.How Much Taller?Given two sets of data about heights, students determine how much taller one group is than the other.Coin Jar Students determine the contents of a coin jar by sampling.Project Work TimeStudents can choose to work on and complete their project or get help if needed.

Students continue to extend their understanding of compound events by comparing independent and dependent events. This includes drawing the sample space to understand how the first event does or does not affect the second event. Students will solve problems with dependent compound events.Key ConceptsStudents will learn about the differences between dependent and independent events.Events are independent if the outcome of an event does not influence the outcome of the others.Events are dependent if the outcome of an event does influence the outcome of the others.The difference can be observed by drawing a diagram to represent the sample space. For dependent events, the sample space is smaller.Goals and Learning ObjectivesUnderstand the difference between independent and dependent compound events.Draw diagrams for dependent compound events.Solve compound event problems.

Students will begin to think about probability by considering how likely it is that their house will be struck by lightning. They will consider the relative likelihood of familiar events (e.g., outdoor temperature, test scores) on the continuum between impossible and certain. Students will discuss where on the continuum "likely," "unlikely," and "equally likely as unlikely" are.Key ConceptsAs students begin their study of probability, they look at the likelihood of events. Students have an intuitive sense of likelihood, even if no numbers or ratios are attached to the events. For example, there is clearly a better chance that a specific student will be chosen at random from a class than from the entire school.Goals and Learning ObjectivesThink about the concept of likelihood.Understand that probability is a measure of likelihood.Informally estimate the likelihood of certain events.Begin to think about why one event is more likely than another.SWD: Students with disabilities may need additional support seeing the relationships among problems and strategies. Throughout this unit, keep anchor charts available and visible to assist them in making connections and working toward mastery. Provide explicit think alouds comparing strategies and making connections. In addition, ask probing questions to get students to articulate how a peer solved the problem or how one strategy or visual representation is connected or related to another.

This article explores how statistics can be interpreted in different ways to yield different conclusions. It describes the outcome and discussion of two class activities. In the first, the results are interpreted to "show" that taking a group rather than an individual perspective is ultimately beneficial to the individual. In the second, a variation is added "showing" that telling the truth is better that lying. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

This course is a seminar intended for undergraduate students who enjoy solving challenging mathematical problems, and to prepare them for the Putnam Competition. All students officially registered in the class are required to participate in the William Lowell Putnam Mathematical Competition.

We will explore the mathematical strategies behind popular games, toys, and puzzles. Topics covered will combine basic fundamentals of game theory, probability, group theory, and elementary programming concepts. Each week will consist of a lecture and discussion followed by game play to implement the concepts learned in class.

In this class, students use data and systems knowledge to build models of complex socio-technical systems for improved system design and decision-making. Students will enhance their model-building skills, through review and extension of functions of random variables, Poisson processes, and Markov processes; move from applied probability to statistics via Chi-squared t and f tests, derived as functions of random variables; and review classical statistics, hypothesis tests, regression, correlation and causation, simple data mining techniques, and Bayesian vs. classical statistics. A class project is required.

Decision-Making often refers to a multi-stage process that starts with some form of introspection or reflection about a situation in which a person or group of people find themselves. These ruminations usually lead to series of questions that need to be answered, or to a set of data that needs to be collected and analyzed, or to some calculations that need to be performed before someone can be in a position to make informed decisions and take appropriate actions.

In this document, we provide some simple examples of Quantitative Models, which are often found in a decision-making situation. We focus on the use of algebraic equations, probability models, the “Payoff Table” and “Decision Tree” models, to represent situations involving a sequence one or more of decisions over time. Concepts are illustrated with a large set of examples that can be presented during classroom instruction and can be practiced by the students, either individually or in groups, through homework or lab exercises.

This resource consists of a Java applet and expository text. The applet is a simulation of the Monty Hall experiment: a car is behind one door, goats are behind the other two doors. The player chooses a door and then the host opens another door. The player is given the option of switching to the remaining door. The stochastic behavior of the host and the probability of the player switching can be specified.

This lesson teaches students how to make decisions in the face of uncertainty by using decision trees. It is aimed for high school kids with a minimal background in probability; the students only need to know how to calculate the probability of two uncorrelated events both occurring (ie flipping 2 heads in a row). Over the course of this lesson, students will learn about the role of uncertainty in decision making, how to make and use a decision tree, how to use limiting cases to develop an intuition, and how this applies to everyday life. The video portion is about fifteen minutes, and the whole lesson, including activities, should be completed in about forty-five minutes. Some of the activities call for students to work in pairs, but a larger group is also okay, especially for the discussion centered activities. The required materials for this lesson are envelopes, small prizes, and some things similar in size and shape to the prize.

The applets in this section allow users to see how probabilities and quantiles are determined from a Normal distribution. For calculating probabilities, set the mean, variance, and limits; for calculating quantiles, set the mean, variance, and probability.

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis.

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB® programming.

PowerPoint Slides to accompany Chapter 3 of OpenStax Statistics textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Statistics textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

This course presents highlights of the more technical side of philosophy. It studies a cluster of puzzles, paradoxes, and intellectual wonders — from the higher infinite to Gödel’s Theorem — and discusses their philosophical implications.

Claude Shannon's idea of perfect secrecy: no amount of computational power can help improve your ability to break the one-time pad. Created by Brit Cruise.

The students will play a classic game from a popular show. Through this they will see the probabilty that the ball will land each of the numbers with more accurate results coming from repeated testing.