Day 17: Data and Probability Goal: To find the probability of independent or dependent events AND To solve problems involving permutations and combinations. Standard: – Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities. Guiding Question: How can I find the probability of an event? AND How can I determine the amount of times an event will occur? Materials: Pencil, Folder, Student Packet 1

Conversions: How many feet are in 3.5 yards? "When converting make sure your labels cancel” Time: "The short hand on the clock gives the hour, the long hand gives the minute" Find the perimeter: "Perimeter is the distance around an object" Reflection Starters: “I know……” or “I need to work on……” Math Review Day 17 Menta l Math 2

Access: Find the theoretical probability of each outcome. A)rolling a 6 on a number cube B) rolling on an odd number on a number cube C) flipping a coin and it landing heads up 3

Independent Event: Dependent Event: Tell whether each set of events is independent or dependent. Explain your answer. : A)You select a card from a standard deck of cards and hold it. A friend selects another card from the same deck B)You flip a coin and it lands heads up. You flip the same coin and it lands heads up again. 4

Try: Tell whether each set of events is independent or dependent. Explain your answer, A)A number cube lands showing an odd number. It is rolled a second time and lands showing a 6. B) One students in your class is chosen for a project. Then another student in the class is chosen. 5

Probability of Independent Events: If A and B are independent events, then P(A and b) = P(A) P(B) A) An experiment consists of randomly selecting a marble from a bag, replacing it and selecting another marble. The bag contains 3 red marbles, and 12 green marbles. What is the probability of selecting a red marble, and then a green marble? B) A coin is flipped 4 times, what is the probability of flipping 4 heads in a row? 6

Try: An experiment consists of spinning the spinner twice. What is the probability of spinning two odd numbers? 7

Probability of Dependent Events: If A and B are dependent events, then P(A and B) = P(A) P(B after A) A) A snack cart has 6 bags of pretzels and 10 bags of chips. Grant selects a bag at random, and then Iris selects a bag at random. What is the probability that Grant will select a bag of chips? 8

Try: A bag has 10 red marbles, 12 white marbles and 8 blue marbles. Two marbles are randomly drawn from the bag. What is the probability of drawing a blue marble and then a red marble? 9

Fundamental Counting Principle: If there are m ways to choose a first item and n ways to choose a second item after the first item has been chosen, then there are mn ways to choose both items. A) A voic system password is 1 letter followed by a 3-digit number less than 600. How many different voic passwords are possible? 10

Try) A sandwich can be made with 3 different types of bread, 5 different meats and 2 types of cheese. How many types of sandwiches can be made if each sandwich consists of one bread, one meat, and one cheese? 11

Compound Event: Combination: Permutation: 12

Tell whether each situation involves combinations or permutations. Then give the number of possible outcomes. A)An English test contains 5 different essay questions labeled A, B, C, D and E. You are supposed to choose 2 to answer. How many different ways are there to do this? B) A family of 3 plans to sit in the theater. How many ways can the family be seated in 3 seats 13

Try: A)Ingrid is stringing three different types of beads on a bracelet. How many ways can she use one bead of each type to string the next three beads? B) Nathan wants to order a sandwich with two of the following ingredients: mushroom, eggplant, tomato and avocado. How many different sandwiches can Nathan choose? 14

Factorial: A) Four people need to be selected from a class of 15 to help clean up campus. How many different ways can the 4 people be chosen? 15

Try: A basketball team has 12 members who can play any position. How many different ways can the coach choose 5 starting players? 16

Exit Slip: (on a half-sheet of scratch paper) A)Tell whether the set of events is independent or dependent and explain your answer: flipping two different coins and each coin landing showing heads B)Eight cards are numbered from 1 to 8 and placed in a box. ne card is selected at random and not replaced. Another card is randomly selected. What is the probability that both cards are greater than 5? C) You are ordering a triple-scoop ice-cream cone. There are 18 flavors to choose from and you don’t care which flavor is on the top, middle, or bottom. How many different ways can you selected a triple-scoop ice-cream cone? 17