Warm up!If you flip a coin 6 times, how many different outcomes are there?

Slides:

Advertisements

Similar presentations

DM. 13. A method for counting outcomes of multi-stage processes If you want to perform a series of tasks and the first task can be done in (a) ways, the.

Advertisements

12-1 and 12-2 Permutations and Combinations Get out that calculator!!

Chapter 8 Counting Principles: Further Probability Topics Section 8.3 Probability Applications of Counting Principles.

Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 15 Chances, Probabilities, and Odds 15.1Random Experiments and.

Counting Principles The Fundamental Counting Principle: If one event can occur m ways and another can occur n ways, then the number of ways the events.

Statistics Review. Box-and-Whisker Plots The Parts of a Box and Whisker Plot Name the parts of a Box-and-Whisker Plot MedianUpper Quartile Lower.

How many possible outcomes can you make with the accessories?

Counting (Combinatorics) 1.

Probability Review Jeopardy!! Jeopardy!! Misc. Compound Events Permutations / Combinations Counting Principle Simple Events.

Today Today: Reading: –Read Chapter 1 by next Tuesday –Suggested problems (not to be handed in): 1.1, 1.2, 1.8, 1.10, 1.16, 1.20, 1.24, 1.28.

Permutations and Combinations AII Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish.

Expected value a weighted average of all possible values where the weights are the probabilities of each outcome :

Permutations and Combinations

Permutations and Combinations. Random Things to Know.

4. Counting 4.1 The Basic of Counting Basic Counting Principles Example 1 suppose that either a member of the faculty or a student in the department is.

Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 15 Chances, Probabilities, and Odds 15.1Random Experiments and.

Advanced Math Topics Chapters 4 and 5 Review. 1) A family plans to have 3 children. What is the probability that there will be at least 2 girls? (assume.

Chapter 8 Counting Principles: Further Probability Topics Section 8.2 Combinations.

Probability Topic 5: Probabilities Using Counting Methods.

Some lovely and slightly random facts… Give the number of objects described. 1. The number of cards in a standard deck The number of cards of each.

Chapter 4 Lecture 4 Section: 4.7. Counting Fundamental Rule of Counting: If an event occurs m ways and if a different event occurs n ways, then the events.

Finding Probability Using Tree Diagrams and Outcome Tables

1/31/2007 Pre-Calculus Chapter 9 Review a n = a 1 + (n – 1)d a n = a 1 r (n – 1)

1 Combinations. 2 Permutations-Recall from yesterday The number of possible arrangements (order matters) of a specific size from a group of objects is.

Probability Jeopardy Final Jeopardy Simple Probabilities Permutations or Combinations Counting Principle Binomial Geometric Probability Potpourri Q $100.

Quiz 10-1, Which of these are an example of a “descrete” set of data? 2.Make a “tree diagram” showing all the ways the letters ‘x’, ‘y’, and ‘z’

Prob/Stats Definition A permutation is an ordered arrangement of objects. (For example, consider the permutations of the letters A, B, C and D.)

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

March 10,  Counting  Fundamental Counting principle  Factorials  Permutations and combinations  Probability  Complementary events  Compound.

Honors Precalculus: Do Now 1.) A game consists of rolling a die. You receive the face value in dollars if an odd number is rolled. If the game costs $1.50.

Ch Counting Principles. Example 1  Eight pieces of paper are numbered from 1-8 and placed in a box. One piece of paper is drawn from the box, its.

The Wonderful World… of Probability. When do we use Probability?

Permutations and Combinations

Permutations and Combinations. Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish permutations.

Suppose I have two fair dice.

Copyright © Ed2Net Learning Inc.1. 2 Warm Up Tell whether each event is dependent or independent 1. Selecting a name from a Chicago telephone book and.

Honors PreCalculus: Section 9.1 Basic Combinatorics.

Lesson 0.4 (Counting Techniques)

Day 17: Data and Probability Goal: To find the probability of independent or dependent events AND To solve problems involving permutations and combinations.

I CAN: Use Permutations and Combinations

37. Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

 Counting  Fundamental Counting principle  Factorials  Permutations and combinations  Probability  Complementary events  Compound events  Independent.

8.6 Counting Principles. Listing Possibilities: Ex 1 Eight pieces of paper are numbered from 1 to 8 and placed in a box. One piece of paper is drawn from.

Algebra-2 Counting and Probability. Quiz 10-1, Which of these are an example of a “descrete” set of data? 2.Make a “tree diagram” showing all.

Permutations and Combinations

Copyright © 2009 Pearson Education, Inc. Chapter 11 Understanding Randomness.

Permutations and Combinations AII Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish.

Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

13 Lesson 1 Let Me Count the Ways Fundamental Counting Principle, Permutations & Combinations CP Probability and Statistics FA 2014 S-ID.1S-CP.3S-CP.5.

Warm up How many ways can 8 children be placed on a 8- horse Merry-Go-Round? 7! = What if Simone insisted on riding the red horse? Here we are only.

Permutations and Combinations

Counting Principles Ex. Eight pieces of paper are numbered 1 to 8 and placed in a box. One piece of paper is drawn from the box, its number is written.

Permutations and Combinations

Permutations and Combinations

Counting, Permutations, & Combinations

Permutations and Combinations

Lesson 11-1 Permutations and Combinations

Permutations and Combinations

Chapter 3.1 Probability Students will learn several ways to model situations involving probability, such as tree diagrams and area models. They will.

Permutations and Combinations

How many possible outcomes can you make with the accessories?

Counting Methods and Probability Theory

Bellwork Practice Packet 10.3 B side #3.

Counting Methods and Probability Theory

Permutations and Combinations

Standard DA-5.2 Objective: Apply permutations and combinations to find the number of possibilities of an outcome.

Permutations and Combinations

Lecture 7: Permutations and Combinations

Permutations and Combinations

Presentation transcript:

Warm up!If you flip a coin 6 times, how many different outcomes are there?

And for your exams… …the average was a 76%… …the median was a 84%… …and on average, students lost CRAZY points on questions 9-17.

The Wørd

Section 8.6 Counting Principles

Slips of paper with the numbers 1-20 inclusive are placed into a hat. How many ways can you pick an odd number? So I have only taught this… A prime number? A prime or an odd number?

An integer divisible by 5? …twice in seven years of teaching. Two integers whose sum is 8? Slips of paper with the numbers 1-20 inclusive are placed into a hat.

Permutations A permutation of n things is an ordering of the elements such that ORDER MATTERS, and there is a first, second, third, and so on. Here is time number three… But there’s an easier way to think about these…

In how many different ways can a 10 question MC exam be answered if each question has 5 answers? …and I really hope…

There are five people waiting in line for one bathroom. In how many different ways can they go #2? …I don’t screw this up too badly.

You’re at Six Flags with three friends. You’re all going to ride the Log thingie at the same time, but you’re the only one that won’t sit in front. In how many ways can you all sit in the log? I’m actually a li’l jealous of Hopkins…

The state of Missouri has license plates that consist of three letters and then three numbers. How many different license plates can the state have? …not only because she has much more experience teaching this…

Distinguishable Permutations Suppose a set of n objects has n 1 of one kind of objects, n 2 of a second kind, n 3 of a third and so on. The number of distinguishable permutations is: …but also because she owns Settlers of Cattan.

In how many distinguishable ways can the letters in the word “Google” be written? I can’t think of a better way…

…to learn and practice probability… In how many distinguishable ways can the letters in the word “Parallelogram” be written?

…than by playing a board game. Combinations The number of combinations of n things taken r at a time is given by:

And even better yet… Five people are running for three spots on a school committee. How many different committees are possible?

…Settlers is not just any board game. How many different five card poker hands are possible?

It’s a game of strategy, deceit, and betrayal. So how do you know when to use a Permutation or a Combination?

I’m pretty good at all of those things… 8 boys and 6 girls are applying to be in Mr. Wu’s Super-Awesome Club. If he can only take 4 guys and 4 girls, how many different ways can Mr. Wu select his club members?

…especially the deceit and betrayal. You are playing Risk, and rolling 5 dice at the same time. How many possible outcomes are there?

And there are few things in life… How many different distinguishable permutations are there of the word basketball?

…better than lording a Settlers win… You are playing a game that requires you to drawr two cards from a deck, roll one dice, and flip two coins. How many outcomes are there?

…over one of your mortal enemies. You are trying out for the first ever PSH co-ed cricket team. Thirty other students are also trying out, and the roster has a limit of 16 players. How many different teams are possible?

8.6: from the packet! And your homework!