Data Analysis & Probability Counting Techniques & Probability (Notes)
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1 Data Analysis & Probability Counting Techniques & Probability (Notes) Name I can Date Essential Question(s): Key Concepts Notes Fundamental Counting Principle Factorial Permutations Combinations What is the difference between the fundamental counting principle, permutations, & combinations? How do you know which formula to use? What are some key concepts to look for or think about within the question? EXAMPLES 1. Lacie has joined a book club. She can choose 4 free books from a list of 12 books. How many different ways can Lacie choose her free books?
2 2. Marina packed a blue denim shirt, a red striped shirt, a red plaid shirt, and a black tank top to take on vacation. She also packed one pair of denim shorts, one pair of white shorts and one pair of beige shorts. Marina took two different pairs of shoes with her. How many different combinations of outfits with one shirt, one pair of shoes and one pair of shorts could Marina use on her vacation? 3. How many ways are there to arrange 7 books in order on a bookshelf? 4. Greg, Haven, Arys, and JaVontae are each signing a solo in a school concert. In how many ways can the four students be listed as the first, second, third, or fourth performer on the program? Outcome Event Probability of an Event When reading questions that deal with probability, it very important to understand what the question is asking. Key concepts that one should look for while reading and the differences between them: Understanding how many events you are doing: The word And and the word Or With or Without replacement:
3 5. A spinner has 8 equal sectors, numbered 1 through 8. If the spinner is spun only one time, what is the probability that it will land on an odd number or a number less than 5? 6. Mandell has a jar full of change. He pulls out four handfuls of change. The table at the right shows how many of each coin he pulled from the jar. Calculate the probability of reaching into the jar and pulling out a quarter? 7. In a bag, there are 2 blue marbles, 3 white marbles, 5 green marbles, and 2 red marbles. Find the probability that you will draw: a) A white marble b) A red or white marble 8. Without replacement, Eric picks two marbles from a basket containing 14 white marbles and 6 yellow marbles. What is the probability that he picks two yellow marbles? 9. Robert has 3 red, 4 white, 2 blue, and 5 green T- shirts in his drawer. He picks a red shirt on Monday without looking. He notices a stain and puts the shirt in the wash. Without looking, Robert then picks another shirt from his drawer. What is the probability he will pick a red shirt on his second try?
4 10. There are eight students in the Algebra Club at Central High School. The students are going to stand in a line for their yearbook picture. How many different ways could eight students stand for their picture? 11. At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey, or ham; and either chips, a brownie, or fruit. Determine the number of possible sandwich combinations. 12. The computer company, Computers-R-Us sells custom made computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? Summary, Reflection, & Analysis
5 Data Analysis & Probability Counting Techniques & Probability (Exercises) Name Date 1. One style of jacket comes in three sizes: small, medium or large. These jackets have either buttons or a zipper. The jackets are available in five different colors. How many different combinations of this jacket are available? 2. Michelle picked a colored cube from a bag of cubes, recorded the color and returned the cube to the bag. She did this 10 times. The table below shows the color of each cube as it was selected. Using the information from the table, how many times would a yellow cube be expected in 30 picks? 3. Aaron and Reno emptied a bag of 100 colored candies and counted the number of each candy. The results are shown in the table. They returned all the candies to the bag. Aaron removes 5 candies, 2 of which are blue. Reno then pulls out one candy. What is the probability that Reno pulls out a blue candy? 4. Brandon bought 4 new books today. He plans to read 2 of these while on vacation. How many combinations of 2 books from the group of 4 books could he choose to read?
6 5. Ricardo is selecting a menu for a party. He plans to select a meal that includes one main dish, one vegetable and one dessert from the following list of choices. How many different meals can Ricardo select? 6. Jack has a box with 10 unlabeled computer CD-ROMs. He knows that 2 are music CDs, 3 are game CDs, and 5 are picture CDs. Jack randomly selects a CD from the box. Which value represents the probability that the selected CD is a music or picture CD? 7. Casey has one afternoon to run errands involving buying a sweater, mailing a package and buying groceries. There are 3 clothing stores, 2 post offices and 4 grocery stores within a 10-mile radius. How many combinations of 1 clothing store, 1 post office and 1 grocery store are available within a 10-mile radius? 8. The table below shows the number of fish caught each day last week. If one day of that week is chosen at random, what is the probability that at least one fish was caught that day?
7 9. Each week, Ms. Haroma has each of the 25 students in her class write his or her own name on a piece of paper. All the pieces of paper are put in a jar and 1 student s name is drawn from the jar. If Jamie s name was drawn last week, what is the probability that it will be drawn again this week? 10. Drake s school awarded 450 raffle tickets as incentives. The principal will draw one winning ticket. The winner will receive a CD player. Drake received 3 tickets for good attendance, 5 for making the honor roll, and 2 for tutoring other students. What is the probability that one of Drake s tickets will be selected by the principal? 11. A banquet center offers a choice of 3 salads, 5 main courses and 4 desserts. How many different meals can be created by selecting one salad, one main course and one dessert? 12. Joel plays tic-tac-toe on his computer. The computer plays first and randomly places an X in one of the grid squares as labeled in the diagram. The frequency table shows the computer s first move for 50 games. Based on these results, what is the experimental probability that the computer will place an X in a corner square on the first move of its next game?
8 13. Luca randomly chose a marble from a bag, recorded the color and replaced the marble before choosing again. The table shows the number of times each color of marbles was chosen. According to the data in the table, what is the experimental probability of picking a green marble? 14. Leroy has a number cube with sides labeled 1 through 6. He tosses the number cube 4 times. Each toss results in a 5. What is the likelihood that the next toss will result in a 5? 15. Population data for Ohio is provided in the table below. Based on the data, what is the probability, rounded to the nearest ten thousandth, that a male selected at random in Ohio in 1998 would have been Hispanic?
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