Lesson 7-1. Warm-up You are at a restaurant with a special for $10. You have the option to get: a) an appetizer and an entree or b) an entree and a dessert.

Slides:



Advertisements
Similar presentations
WonLost 1234 Year Number of Games Warm-Up 1) In which year(s) did the team lose more games than they won? 2) In which year did the team play.
Advertisements

UNIT 4: Applications of Probability UNIT QUESTION: How do you calculate the probability of an event? Today’s Question: What is a permutation or combination.
Probability Jeopardy Final Jeopardy Simple Probabilities Permutations or Combinations Counting Principle Fractions Decimals Spinners Potpourri Q $100.
Counting (Combinatorics) 1.
Warm Up Use an inequality symbol to make each expression true a x 10 4 ___________ 5, 430 b. 32 ÷ ¼ ___________ 32 ÷4 c. 0.72___________¾.
Probability Using Permutations and Combinations
6-7 Permutations & Combinations M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle.
4.1. Fundamental Counting Principal Find the number of choices for each option and multiply those numbers together. Lets walk into TGIF and they are offering.
Probability Jeopardy Final Jeopardy Simple Probabilities Permutations or Combinations Counting Principle Find the Probability Independent Dependent Q.
Combinations and Permutations
WonLost 1234 Year Number of Games Warm-Up 1) In which year(s) did the team lose more games than they won? 2) In which year did the team play.
Math Review 1. Ashton is drawing a map of the trails at the Grand Canyon. If she wants 1 mile to be 2.5 inches on her map, then how many inches would represent.
Permutations and Combinations Multiplication counting principle: This is used to determine the number of POSSIBLE OUTCOMES when there is more than one.
Formulas and Principles. Math I Unit 4 If one event can occur in m ways and another event can occur in n ways, then the number of ways that both events.
Probability Jeopardy Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy
(13 – 1) The Counting Principle and Permutations Learning targets: To use the fundamental counting principle to count the number of ways an event can happen.
Holt CA Course Disjoint Events SDAP3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual.
Day 18 Basic Counting Rule. Probabilities Related concepts: Experiment, Event, Sample Space If we assume all sample points are equally likely, the probability.
CONFIDENTIAL 1 Algebra1 Combinations and Permutations.
Fundamental Counting Principle Probability. Tree Diagrams (remember how to draw these?) You have a photo that you want to mat and frame. You can choose.
Chapter 7 Probability Practice Lessons 1-4 And Ch 8 less 6 Mrs. Parziale.
Lesson # 64 – 65 Notes Permutations and Combinations 1.The Counting Principle – The number of outcomes for an event is the product of the number of outcomes.
Permutations, Combinations, and Counting Theory AII.12 The student will compute and distinguish between permutations and combinations and use technology.
The Fundamental Counting Principle states that if there are x ways to choose a first item and y ways to choose a second item, then there are x(y) ways.
Probability Jeopardy Final Jeopardy Simple Probabilities Independent & Dependent Events Counting Principle Fractions Decimals Spinners Misc. Q $100 Q.
Probability Jeopardy Final Jeopardy Simple Probabilities Permutations or Combinations Counting Principle Binomial Geometric Probability Potpourri Q $100.
Today’s Lesson: What: probability of compound events Why: To create and analyze tree diagrams; discover and use the fundamental counting principle; and.
Section 6.1 Use Counting Principles. Vocabulary The Multiplication Counting Principle: 1 event can occur in m ways another event can occur in n ways both.
THE COUNTING PRINCIPLE (ch 8.7 in the textbook) Goal: to use the counting principle to count the number of ways an event can happen.
 Roll a die, flip a coin  Unique 3 letter arrangements of CAT  Unique 4 digit arrangements of 1, 2, 3, 4.
Let’s work on some definitions Experiment- is a situation involving chance that leads to results called outcomes. An outcome is the result of a single.
Unit 2 - Permutations and Organized Counting
The Fundamental Counting Principle 10-6 Learn to find the number of possible outcomes in an experiment.
Tues 9/4 & Wed 9/5 AGENDA Warm up text p.805; Go over homework Test Review Game Go over review packet.
Discrete Mathematics, 1st Edition Kevin Ferland Chapter 6 Basic Counting 1.
Probability & Statistics The Counting Principle Section 12-1.
Fundamental Counting Theorm. Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when.
Permutations, Combinations, and Counting Theory
Bellwork Maria has an unidentified disease. She has the option to choose from three states in which to be treated. In each state, there are two research.
The Counting Principle Uses multiplication to find the number of possible ways two or more events can occur.
DAY 6: FUNDAMENTAL COUNTING PRINCIPLE Classwork: pptx examples in class Discrete Pre- Test (not a grade in HAC) Unit 2 Project- Due day 13 Homework (day.
Designing A Menu. Importance of The Menu The menu style and design reflects the restaurant’s personality and the customers who frequent it. The menu can.
Probability of Simple Events
Multiplication Counting Principle How many ways can you make an outfit out of 2 shirts and 4 pants? If there are m choices for step 1 and n choices for.
A local restaurant is running a lunch special where you can purchase a lunch combo for $5.00. This combo includes a soup, a salad, and a drink. Here are.
Chance of winning Unit 6 Probability. Multiplication Property of Counting  If one event can occur in m ways and another event can occur in n ways, then.
Warm Up For a main dish, you can choose steak or chicken; your side dish can be rice or potatoes; and your drink can be tea or water. Make a tree diagram.
WonLost 1234 Year Number of Games Warm-Up 1) In which year(s) did the team lose more games than they won? 2) In which year did the team play.
Introduction to Probability Honors Geometry Summer School.
Multiplication Counting Principle How many ways can you make an outfit out of 2 shirts and 4 pants? If there are m choices for step 1 and n choices for.
Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.
Bell work Diagnostic Evaluation Please pick up a Pre-Assessment off the table as you come in to class, take a seat, and get started.
THE COUNTING PRINCIPLE CHAPTER 12 LESSON 1. VOCABULARY Outcome- The result of a probability experiment or an event. Sample Space- The set of all possible.
Preview Warm Up California Standards Lesson Presentation.
Topic: Probability Aim: How do we find the probability of compound events? Do Now: Three-course dinners can be made from the menu shown. (a) Find the sample.
Probability of compound events
Counting Principles and Tree Diagrams
How to Count Things “There are three kinds of people in the world: those who can count and those who cannot.” 11/21/2018.
Homework Review.
Homework Review.
Probability Simple and Compound Probability
Probability Warm Up page 12- write the question you have 10 mins to complete it. See coaching on page 85.
Warm-Up Year Year 1 Year 2 Year 4
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
The Counting Principle & Finding Sets
Determining the Number of Possible Outcomes
Probability By Mya Vaughan.
Probability Warm Up page 12- write the question you have 10 mins to complete it. See coaching on page 85.
Fundamental Counting Theorm
Module 1 Unit 2 What do you want to eat?
Presentation transcript:

Lesson 7-1

Warm-up You are at a restaurant with a special for $10. You have the option to get: a) an appetizer and an entree or b) an entree and a dessert. There are 3 options for appetizers, 4 options for entrees, and 2 options for dessert. How many different meals can you make out of option a? Out of option b? How many total different meals can you make with the special?

Addition Counting Principle If the possibilities being counted can be divided into groups with no possibilities in common, then the total number of possibilities is the sum of the numbers of possibilities in each group. If the possibilities being counted have common possibilities, P(A or B) = P(A) + P(B) – P(A and B)

Addition Counting Principle Example: For lunch in the cafeteria, you can either have a milk or a juice with your meal. If there are 3 different types of milk and 4 types of juice, how many different choices do you have?

Addition Counting Principle Example: You are playing crazy eights and could put down either a 5 or a heart. How many different cards will satisfy these conditions?

Multiplication Counting Principle If one event can occur in m ways and another event can occur in n ways, then the number of ways that both events can occur together is m x n. This principle can be extended to 3 or more events.

Multiplication Counting Principle Example: The drama club is holding tryouts for a play. With six men and eight women auditioning for the leading roles, how many different couples could be made?

Question 1 It's election time at school. 5 people are running for president, 3 people are running for vice-president, and 6 people are running for treasurer. How many different combinations of officers could you have in charge of your class?

Question 2 In a town, each person gets a different telephone number. If no telephone number can start with a 0 or a 1, how many different 7-digit telephone numbers can be registered in that town?

Question 3 A alpha-numeric code can either be 2 digits (numbers) followed by 1 letters or 2 letters followed by 1 digit. How many different codes can you make?

Use the Addition Principle of Counting Example: Every purchase made on a company’s website is given a randomly generated confirmation code. The code consists of 3 symbols (letters and digits). How many codes can be generated if at least one letter is used in each?

Solution: To find the number of codes, find the sum of the numbers of possibilities for 1-letter codes, 2-letter codes, and 3-letter codes. 1-letter: There are 26 choices for each letter and 10 choices foe each digit. So there are 26x10x10 = 2,600 letter-digit-digit possibilities. The letter can be in any position so there are 3x2,600 = 7,800 possibilities. 2 letter: There are 26x26x10 = 6,760 letter-letter-digit possibilities. The digit can be in any of the three positions, so 3x6760 = 20,280 possibilities. 3 letter: There are 26x26x26 = 17, 576 letter-letter-letter possibilities. So there are 7, , ,576 = 45,656 possible codes

Let’s Recall… What is Probability?!?!?

How does this apply to probability? Let’s take another look one of the last problems: An alpha-numeric code can either be 2 digits (numbers) followed by 1 letter or 2 letters followed by 1 digit. What is the probability that if you picked a code at random, it would end with a “Z”?

Finding the Probability You are having lunch at a restaurant. You order the special from the menu shown. If you randomly choose the soup and sandwich, what is the probability that your order includes vegetable soup. Lunch Special $5.95 Choose 1 soup and 1 sandwich Soups Sandwiches French Onion Chicken VegetableClub Grilled Cheese

Finding the Probability Solution: Because there are 2 soup choices and 3 sandwich choices, the total number of possible lunch orders is 2x3 = 6. If you limit yourself to only 1 soup, vegetable soup, then the number of orders that include vegetable soup 1x3 = 3

Solving a multi-step problem Playing a game, you and four friends each roll a six- sided number cube. What is the probability that you each roll the same number?

Solving a Multi-step problem Step 1: List the favorable outcomes. There are 6: Step 2: Find the total number of outcomes using the multiplication principle. Total number of outcomes = 6x6x6x6x6 = 7,776 Step 3: Find the probability.

Let’s Practice You walk into an ice cream store… There are 40 different types of ice cream and 20 different types of soft drinks. You are only allowed to buy one item from the store. How many different choices do you have for either ice cream or soft drinks? = 60

Let’s Practice The same ice cream store has 40 different types of ice cream…and they also have a choice of 3 different toppings!! How many different combinations of ice cream and toppings can you have from this ice cream store? Using the multiplication principle of counting we get 120 different choices.

Let’s Practice A Chinese restaurant serves 25 rice dishes and 10 noodle dishes. If Simon orders either a rice dish or a noodle dish, from how many dishes can he choose? = 35

Let’s Practice Abby has 3 hats, 4 scarves, and 3 pairs of gloves. In how many different ways can she wear a hat, a scarf, and a pair of gloves? 3 * 4 * 3 = 36

Let’s Practice A pirate walk into a bar…he has a choice of 3 different places to sit, 4 different items to drink, and 10 different items to eat. How many different combinations does the pirate have of sitting, drinking, and eating? 3*4*10 = 120

Let’s Practice The cafeteria serves 8 dishes that have meat in them and 4 that do not. How many different choices of food would you have if you were to buy lunch from this cafeteria? 8+4 = 12