May or May Not? Probability & Statistics

Transcription

1 May or May Not? Probability & Statistics Lessons & Activities for probability 2013 Lindsay Perro Clipart by Scrappin Doodles

2 Probability & Statistics Lesson Outline: o Week One Probability Notes Compound Events Notes Multiple Choice Practice Activity o Week Two Probability Activities What Are The Chances? Activities o Week Three Simulations Notes Simulations Practice Three activities o Week Four Probability Quiz Independent and Dependent Probability Probability PowerPoint Practice Independent, Dependent and Compound Probability Simulations and Samples PowerPoint Practice

3 Week 1

4 Probability Notes KEY WORDS: Probability is a measure of the likelihood, or chance, that an event will occur. Outcomes are the possible results of an experiment. An event is an outcome or a collection of outcomes. Sample Space is the set of all possible outcomes. A tree diagram is a visual way to find the number of outcomes. A tree diagram is not a good method to determine number of outcomes if you are dealing with a large number of possibilities. The counting principal is a mathematical way to determine the number of outcomes. A simulation is an experiment that you can perform to make predictions about real-world situations. TYPES OF PROBABILITY: Theoretical Probability = Experimental Probability =

5 Name Date ODDS VS. PROBABILITY Probability is a measure of the likelihood, or chance, that an event will occur. Odds compare the number of favorable and unfavorable outcomes. When determining odds, you do not use the total number of outcomes. Odds in Favor = Odds Against = PRACTICE OUTCOMES Determine the number of possible outcomes in the sample space. You toss a coin. A bag contains 5 blue cards and 4 red cards. You toss a coin and roll a dice. You toss two coins. You want to select a person at random from your family.

6 THEORETICAL PROBABILITY Use the spinner to the right to answer the questions below. Express each probability as a fraction in lowest terms. 1. What is the probability that the spinner stops on red? 2. What is the probability that the spinner stops on a color other than blue? 3. What is the probability that the spinner stops on a number greater than 10? 4. You spin the spinner 20 times. It stops on green twice. What is the experimental probability of stopping on green? 5. You spin the spinner 100 times. It stops on red 40 times. What is the experimental probability of stopping on red? 6. What are the odds in favor of stopping on the number 100? 7. What are the odds against stopping on blue?

7 You are making greeting cards and selling them to friends. You use blue paper and pink paper. You also use crayons or markers. Your friends pick a greeting card at random from your bag. Crayon Marker Blue paper 7 6 Pink paper What is the probability that your friend chooses a pink card? 2. What is the probability that your friend chooses a card made with crayons? 3. What is the probability that your friend chooses a pink card with marker? 4. What are the odds against picking a blue card with crayon? 5. What are the odds in favor of picking a pink card with crayon?

8 Name Date KEY WORDS: Compound Event - Probability of Compound Events Notes Mutually Exclusive Event Overlapping Events Independent Events Dependent Events Finding the probability of A OR B. The word OR means to ADD! Example : You roll a dice. What is the probability you roll and even number or a three? Step 1 Find the probability of each event. The probability of rolling an even number is The probability of rolling a three is Step 2 Add the two probabilities. Always simplify if necessary. + =

9 Finding the probability of A AND B. The word AND means to MULTIPLY! Example : You roll two dice. What is the probability you roll a 2 and a 5? Step 1 - Determine whether or not the events are independent or dependent Why? Step 2 Find the probability of each event. The probability of rolling a 2 on one dice The probability of rolling a 5 on the other dice Step 3 Multiply the two probabilities. Always simplify if necessary + = Example : You pick a piece of candy out of a jar. There are 5 strawberry pieces, 4 orange pieces, 3 cherry pieces and 6 banana pieces. You choose a strawberry piece. Your friend chooses a cherry piece. What is the probability of picking a strawberry and then a cherry piece? Step 1 - Determine whether or not the events are independent or dependent Why? Step 2 Find the probability of each event. The probability of picking a strawberry candy The probability of picking a cheery candy (remember, one is gone!) Step 3 Multiply the two probabilities. Always simplify if necessary + =

10 Quick check for understanding! Show your work. 1. You roll a dice. What is the probability you roll a 3 or a 6? 2. You roll a dice and flip a coin. What is the probability you get an even number and land on tails? 3. A drawer contains 6 red socks, 4 white socks, and 8 black socks. What is the probability you grab a red or a black sock? 4. A drawer contains 6 red socks, 4 white socks, and 8 black socks. What is the probability you grab a white sock, put it back and then grab a red sock? 5. A drawer contains 6 red socks, 4 white socks, and 8 black socks. What is the probability you grab a black sock, do not return it to the drawer, and then grab a white sock?

11 Probability Practice Solve each problem. Find your answer in one of the three answer boxes. # Answer 1 Answer 2 Answer You flip a coin and roll a dice. What is the probability the coin lands on heads and the dice lands on a number less than 5? You have 20 shirts in your closet. 4 blue, 7 red, 3 green and 6 black. You pick one without looking. What is the probability that you pick a blue or black shirt? 1/3 7/6 5/8 1/4 1/2 3/ of the last 30 cars that passed you were black. What is the probability the next car will be black? Five out of 8 bags of M&Ms had exactly 32 pieces in them. How many bags out of 40 should have exactly 32 pieces? There are 18 girls and 12 boys in your class. What is the probability that a new kid entering your class will be a boy? Barb ate six cheeseburgers in the last four months. How many do you predict she will eat in two years? 8/10 of the people at the circus are kids. If 575 tickets were sold, how many are expected to be kids? ,035 8 A four sectioned spinner is numbered 1-4. What is the probabilty you spin a 2, and then a 4? You roll two dice. What is the probability you get a 2 and a number greater than 2? 1/3 1/9 1/36 10 John has opened 8 gifts and 6 of them have been toys. What is the probability that the next gift he opens will be a toy?

12 Week 2

13 Name Date The mathematical probability of an event = Activity 1 Probability Activities # of ways a desired event can occur Total # of possible outcomes 1. If you roll your die, what is the mathematical probability that you will roll the following: Now roll your die twenty times. Use the table to record the twenty numbers you rolled. 3. According to the results found in your experiment, what is the probability of rolling the following: How do your probabilities from Question 1 compare to those in Question 3?

14 Activity 2 1. There are 8 pieces of paper in the bag. Two are orange, Three are green, Two are yellow and one is blue. If you pull a piece of paper from the bag, what is the mathematical probability that the piece will be: Orange Yellow Green Blue 2. Now, pull a piece of paper from the bag. Use the table to record the color, and then put the piece back into the bag. Repeat 11 more times. 3. According to the results found in your experiment, what is the probability of pulling each color? Orange Yellow Green Blue 4. How do your probabilities from Question 1 compare to those in Question 3?

15 Activity 3 1. If you flip a coin, what is the probability it will land on each of the following: Heads Tails 2. Flip your coin 20 times. Record your results below. 3. According to the results found in your experiment, what is the probability of landing on each of the following: Heads Tails 4. How do your probabilities from Question 1 compare to those in Question 3?

16 Activity 4 1. The cuboctahedron has 14 sides. What is the probability of rolling it and landing on a: Square Triangle 2. Roll the cuboctahedron 20 times. Record your results below. 3. According to the results found in your experiment, what is the probability of landing on each of the following: Square Triangle 4. How do your probabilities from Question 1 compare to those in Question 3?

17 Activity 5 1. The following letters are in the bag P R O B A B I L I T Y If you pull a letter from the bag, what is the mathematical probability that the letter will be a: P I B L 2. Pull a letter from the bag. Record your results and replace the letter. Repeat 11 more times. 3. According to the results of your experiment, what is the probability of landing on each of the following? P I B L 4. How do your probabilities from Question 1 compare to those in Question 3?

18 Activity 2 Cards Print & Cut ORANGE ORANGE GREEN GREEN GREEN BLUE YELLOW YELLOW

19 Activity 4 Cut & Assemble Prior to Class

20 Activity 5 Cards Print & Cut P R O B A B I L I T Y

21 What Are The Chances? Materials & Directions Materials: One copy of student station worksheet. For Activity 1 a pencil and paper clip to be used for the spinner. For Activity 2 a coin Calculators (optional) Directions: There is no need to actually print any of the Activity pages except for Activity 1 where the students need to use the spinner. All answers can be recorded on the Student Worksheet. Each activity shouldn t take any more than 5 minutes.

22 Activity 1 Brent is getting ready for another season of football! He can t decide what color cleats he wants. He is deciding between black, blue, green, white, red and orange. He makes a 6 section spinner to help him choose. Orange Red Green Using a pencil and a paperclip, spin the spinner 25 times. Black White Record your results in the tally chart on the student worksheet. Blue For problems 1 4, record your answers as fractions, decimals & percents! 1. Based upon the results of your experiment, what is the probability the next spin will land on Red? 2. Based upon the results of your experiment, what is the probability the next spin will land on Orange or Green? 3. Based upon the results of your experiment, what is the probability the next spin will not land on land on White? 4. Based upon the results of your experiment what color cleats will Brent get?

23 Activity 2 Now that Brent has his shoes, he is ready to play! There are two teams he could play on. He decides to flip a coin to pick the team. Heads = Bears Team and Tails = Jaguars Team Help Brent figure out what team to play on. Flip a coin 25 times and record the results in the table on your student worksheet. For problems 5 7, record your answers as fractions, decimals & percents! 5. Based upon the results of your experiment, what is the probability the next flip will land on heads? 6. Based upon the results of your experiment, what is the probability the next flip will land on tails? 7. Based upon the results of your experiment what team will Brent play for?

24 Activity 3 Halfway through the season Brent s team has played 10 games and won 7 of them! 8. Based upon their current record, what is the probability they will win their next game? Express your answer as a decimal. 9. What is the probability they will lose their next game? Express your answer as a percent. 10. Based upon their performance so far, if Brent s team plays 22 games this season, how many should they expect to win? (Round to the nearest whole number.) Brent is the quarterback and is doing a great job! He has thrown the ball 40 times so far this game and has completed passes 32 of those times. 11. Based on his performance so far, what is the probability he will not complete his next pass? Express your answer as a decimal. 12. What percent of his passes have been complete? 13. Based on his performance so far, if Brent throws a total of 120 passes game, how many should he expect to complete?

25 Activity4 After the game everyone on the team gets a snack! There are 20 fruits in a bag; 7 apples, 4 oranges, 5 bananas and 4 bunches of grapes. 14. If Brent picks a fruit from the bag without looking, what is the probability it will be a banana? Express your answer as a fraction in simplest form. 15. What is the probability Brent will pick an apple or an orange? Express your answer as a decimal. 16. Brent picks grapes from the bag. He doesn t like grapes! He puts them back, and without looking, out an orange. What is the probability that would occur? Express your answer as a decimal and a percent. Everyone on the team also gets a drink! There are 25 drinks in a cooler; 11 bottles of water, 10 bottles of Gatorade & 4 bottles of milk 17. What is the probability Brent will pick either a bottle of water or a bottle of milk? Express your answer as a fraction in simplest form. 18. What is the probability Brent will NOT pick a bottle of water? Express your answer as a decimal.

26 Name Date What Are The Chances? Student Station Worksheet Activity 1 Color Green White Blue Orange Red Black Tally Activity 2 Heads Tails Side Tally

27 Activity Activity

28 Week 3

29 What is a simulation? Simulations Notes How do you design a simulation? 1) 2) 3) 4) 5) What can you use to perform simulations?

30 Field Goal Kicker It s the end of the championship football game and the score is tied. The kicker has to make this field goal to win the game. He has a 75% accuracy rate. What is the probability that he will make the field goal and win the game? 1. Label the spinner above to represent a 75% success rate. 2. Hold a paper clip in place with the tip of your pencil and spin the spinner. What does the spin represent? Did he make the kick? 3. Record the results of 30 trials, and estimate the probability that the game is won. Trial Trial

31 Quiz Time Hooray! It s time for a quiz in Science, but you are not at all prepared! The quiz consists of 10 true / false questions. You decide to guess at each response. You need at least 7 correct responses to get a C on the quiz, and you want to estimate the likelihood that you will pass. You will simulate guessing on the test by flipping a coin 10 times. Each coin flip represents one statement on the test. Let heads represent a correct answer, and tails represent and incorrect answer. 1) Toss a coin 10 times and record your results in the table below. Trial Response a) According to your results, how many questions were answered correctly? 2) Toss the coin 10 more times and record your results in the table below. Trial Response a) According to your results, how many questions were answered correctly? 3) Suppose you toss the coin 20 more times. How many correct answers would you expect? 4) Record the results from everyone in the classroom in the table below. # of successes Tally Frequency # of successes Tally Frequency ) Based on the data, what is the probability of guessing the correct response at least 7 times, scoring at least a C on the quiz? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

32 Simulations & Probability Determine which would be the best simulation experiment for each situation. Find your answer in one of the three answer boxes. # Answer 1 Answer 2 Answer 3 1 A goalie saves half of the attempted shots on a goal during a game. Design a simulation to predict how many of 12 shots will be saved. Flip a coin 12 times. Heads is a save, Tails is a miss. Spin a 12 section spinner once. See how many goals you can score in 12 shots. 2 3 A basketball player makes 75% of his free-throw attempts. Design a simulation to predict how many free throws he will make if he attempts 20 in a game. A true / false quiz has 25 questions. Each question has 2 choices and 1 correct answer. Design a simulation to predict how many answers you will get correct if you guess on each one. Shoot a basketball 20 times. Spin a four sectioned spinner 25 times. Flip a coin 20 times. Heads you make it, Tails you don t. Flip a coin 25 times. Heads is correct and Tails is incorrect. Spin a spinner 20 times that has three 3 blue sections and 1 red. Practice by guessing on a real test in your class! 4 12 candy canes are in a bag. 8 blue and 4 green. You pick one without looking. What is the probability it is green? 1/2 1/3 1/4 5 You reach into your sock drawer without looking. You have 9 white pairs and 11 colored pairs. What is the probability you get a white pair?

33 # Answer 1 Answer 2 Answer There are 25 remaining slots on a field trip. The students are chosen at random to go. If there are 16 boys in your class and 9 girls, what is the probability a girl is chosen first? A candy jar has 40 pieces of candy. 22 are chocolate, 10 are licorice, 5 are lollipops and 3 are taffy. You choose a lollipop and decided to put it back. What is the probability you pull a lollipop and then a piece of chocolate? At a restaurant I can choose from 3 different sizes of pizza, two different types of crust and 6 different toppings. How many different pizzas can I make? /40 11/160 11/ You toss four coins at the same time. What is the probability you land on one head and three tails? You roll three dice at the same time. What is the probability one lands on a 3, the other lands on a number less than 5 and the third dice lands on a number greater than 4? 1/2 1/4 1/16 1/216 1/36 1/27

34 Week 4

35 Probability Quiz 1. You roll two dice. What is the probability that you roll a 2, then a 1? A. B. C. D At the pizza restaurant, you can choose three types of crust, four types of toppings, and get a small, medium or large. How many different types of pizza can be created from these choices? A. 12 B. 24 C. 36 D The probability of snow today is 20% and the probability of snow tomorrow is 50%. What is the probability that it will snow both days? A. 1 B. 3 C. 7 D You have a bag full of candy. There are 22 strawberry candies, 8 apple candies, and 10 orange candies. If you choose a candy at random and put it back in the bag, then choose a second candy, what is the probability that the candies you select will be apple, then orange? A. 0.5 B C D A bag contains 4 red tiles, 3 blue tiles, 2 green tiles, and 1 yellow tile. What is the probability of drawing a blue tile then another blue tile if the first tile is not returned to the bag? A. B. C. D. 6. You toss a coin three times. What is the probability that the coin lands on heads each time? A. B. C. D To set the combination for your lock you need to pick three letters, A-E. You can use each letter more than once. How many possible combinations are there?

36 8. The band has 14 female students and 18 male students. Two students are to be selected at random to perform together. The band director writes each name on a card and places the card in a paper bag. Step A What is the probability that the coordinator will draw the name of a girl followed by the name of a boy? The first name is not replaced before the second name is drawn. Step B Use what you know about finding probability of dependent events to explain why your answer is correct. Use words, numbers, and/or symbols in your explanation.