#### Transcript 6.1 use counting principles

1) In which year(s) did the team lose more games than they won? 2) In which year did the team play the most games? 3) In which year did the team play ten games? Number of Games Warm-Up 10 8 Won Lost 6 4 2 0 1 2 3 Year 4 6.1 The Addition & Multiplication Principles of Counting What are we Learning Today? Determine the number of outcomes related to a given event Determine the number of outcomes related to a given event. Apply the addition and multiplication principle of counting. Calculate and use simple permutations and combinations. The Addition Counting Principle • If the outcome of interest can be divided into groups with no possibilities in common, then the number of possibilities is the sum of the numbers of possibilities in each group. Determine the number of outcomes related to a given event. Apply the addition and multiplication principle of counting. Calculate and use simple permutations and combinations. The Addition Counting Principle Example: • A box contains 5 bags of milk chocolate M&M’s, 5 bags of peanut M&M’s, 5 bags of sour skittles, 5 bags of regular skittles, 5 bags of chocolate covered raisins, and 5 bags of tropical skittles. How many bags are a variety of skittles? 15 Determine the number of outcomes related to a given event. Apply the addition and multiplication principle of counting. Calculate and use simple permutations and combinations. Tree Diagrams Tree diagrams allow us to see all possible outcomes of an event and calculate their probabilities. This tree diagram shows the probabilities of results of flipping three coins. Use an appropriate method to find the number of outcomes in each of the following situations: 1. Your school cafeteria offers chicken or tuna sandwiches; chips or fruit; and milk, apple juice, or orange juice. If you purchase one sandwich, one side item and one drink, how many different lunches can you choose? There are 12 possible lunches. Sandwich(2) Side Item(2) chips chicken fruit chips tuna fruit Drink(3) Outcomes apple juice orange juice milk apple juice orange juice milk chicken, chips, apple chicken, chips, orange chicken, chips, milk chicken, fruit, apple chicken, fruit, orange chicken, fruit, milk apple juice orange juice milk apple juice orange juice milk tuna, chips, apple tuna, chips, orange tuna, chips, milk tuna, fruit, apple tuna, fruit, orange tuna, fruit, milk The 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∙n. • In other words: Multiply the number of choices you have at each stage Determine the number of outcomes related to a given event. Apply the addition and multiplication principle of counting. Calculate and use simple permutations and combinations. The Multiplication Counting Principle Example: 2.) How many different looks can you give Mr. Potato Head if we can choose from: 4 hats, 2 noses, 3 eyes, 2 shoes, and 5 ties? 240 Determine the number of outcomes related to a given event. Apply the addition and multiplication principle of counting. Calculate and use simple permutations and combinations. Multiplication Counting Principle 3.) At a sporting goods store, skateboards are available in 8 different deck designs. Each deck design is available with 4 different wheel assemblies. How many skateboard choices does the store offer? 32 Multiplication Counting Principle 4.) A father takes his son Tanner to Wendy’s for lunch. He tells Tanner he can get the 5 piece nuggets, a spicy chicken sandwich, or a single for the main entrée. For sides: he can get fries, a side salad, potato, or chili. And for drinks: he can get milk, coke, sprite, or the orange drink. How many options for meals does Tanner have? 48 Multiplication Counting Principle 5.) The combination for a briefcase consists of 3 symbols (letters and digits). How many combinations are possible if at least one digit is used? Probability of an event The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. P(A)=Favorable Outcome Total Outcomes P(A)=Favorable Outcome Total Outcomes (Choices) 6.) You and 2 friends each randomly pick a movie from 6 choices. What is the probability that you pick the same movie? P(A)=Favorable Outcome Total Outcomes (Choices) 7.) A code consists of 3 digits (0-9). a.) Find the probability that it starts with one. b.) Find the probability that it only contains even numbers. c.) Find the probability that it uses the same number in each position. TICKET OUT THE DOOR 1.) Make a tree diagram that shows the total number of choices for computer monitors: Type: flat screen, flat panel Size: 15 in., 17 in., 19 in., 21 in. 2.) Use the multiplication principle to answer: You have 9 choices of curtains, 12 choices of paint & 18 choices of carpeting. How many different ways can you decorate your room? 3.) The code to a safe is made up of 4 digits. What is the probability that all 4 numbers are the same? Homework Session 1: Pg. 340 1-13 all