CHAPTER. Probability. Key Word Builder 632. Math Games 633. Challenge in Real Life 634. Answers 636

Transcription

1 CHAPTER Probability GET READY 586 Math Link 588. Warm Up 589. Determining Probabilities Using Tree Diagrams and Tables 590. Warm Up 60. Outcomes of Independent Events 60. Warm Up 60. Determining Probabilities Using Fractions 6 Chapter Review 6 Practice Test 68 Wrap It Up! 6 Key Word uilder 6 Math Games 6 Challenge in Real Life 6 Answers 66

2 Fractions Decimals and Percents To change a fraction to a percent: Step : Change the fraction to a decimal. 5 Divide the numerator by the denominator Step : Change the decimal to a percent % Multiply the decimal by 00 and add the percent sign. Multiplying by 00 is the same as moving the decimal places to the right.. Complete the table. Fraction Decimal (numerator denominator) Percent (decimal 00) a) 8 00 % b) 00 % Probability probability the chance that an event will happen number of probability total number of impossible event 0 or 0% probability (will not happen) certain event or 00% probability (will definitely happen) Find the probability that a coin will land heads up. number of P ( H) total number of number of heads total number of faces What you want to happen. The probability that the coin will land heads up is 0.5 or 50%. 586 MHR Chapter : Probability

3 . You spin the spinner once. What is the probability of spinning a? Write the answer as a fraction a decimal and a percent. P() means the probability of spinning a. P () The probability of spinning a is 0. or %. Using Tables and Tree Diagrams Flip a coin and spin the spinner. You can use a table and a tree diagram to organize the outcomes. Table Tree Diagram Spinner Coin Heads (H) H H H Tails (T) T T T Coin Flip H T Spin Outcome H H H T T T There are 6 : (H ) (H ) (H ) (T ) (T ) (T ).. a) Use a table to show the when you spin this spinner and roll a 6-sided die. A 5 Die Spinner 5 6 A A b) List the outcomes. ( ) Get Ready MHR 587

4 Probability Games Many games use cards or dice. These games use probability. a) Name game that uses cards. b) Do your chances of winning the game depend on how the cards are dealt? Circle YES or NO. c) Explain how you use the cards in the game. d) Name game that uses dice. e) Do your chances of winning the game depend on how you roll the dice? Circle YES or NO. f ) Explain how you use the dice in the game. g) Share your answers with a classmate. Write thing your classmate told you. 588 MHR Chapter : Probability

5 . Warm Up. Change the fractions to decimals and percents. Fraction Example: 9 a) b) 6 Decimal (numerator denominator) 9 0. or 0. The bar over the shows a repeating decimal. Percent (decimal 00) % 00 % 00 % c) 7 9 d). You roll a 6-sided die. Find the probabilities. Write your answer as a decimal. a) P (6) b) P (even number) Even numbers are 6. Divide. Write your answer as a decimal. a) b) Think of dollar divided by. c) 5 d) 0. Warm Up MHR 589

6 . Determining Probabilities Using Tree Diagrams and Tables Working Example : Determine Probabilities From a Tree Diagram independent events or more events that do not affect each other example: spinning a spinner does not affect what happens if you also roll a die a) What is the probability of spinning A on the first spin? Write your answer as a fraction a decimal and a percent. Solution A There are sections on the spinner: A and. How many are there? P (A) How many A s are there? 0. C 0. The probability of spinning A is 0. or.%. b) Draw a tree diagram to show the sample space when you spin the spinner twice. Solution sample space all the of the event Spin Spin Outcomes A A A A A A 590 MHR Chapter : Probability

7 c) What is the probability of spinning A and then spinning P(A then )? Write the answer as a fraction a decimal and a percent. Solution The favourable outcome is (A ). Look at the tree diagram. How many times does (A ) happen? P (A then ) 9 C 9 0. Use bar notation to show a repeating decimal. Spin Spin Outcome A A A A A A A A A A The probability of spinning A and then is 0. or %. d) Use the tree diagram to find the probability of getting the same letter on both spins P(A A) or P( ). Write your answer as a fraction a decimal and a percent. Solution P(A A) or P ( ) How many outcomes are (A A) or ( )? Add the numbers. 9 The probability of spinning the same letter is 0. or %.. Determining Probabilities Using Tree Diagrams and Tables MHR 59

8 You flip a coin and roll a -sided die numbered and. a) Complete the tree diagram to show the sample space. Coin Die Outcomes H T H T b) How many outcomes are there? c) What is P(H )? P (H) decimal Multiply by 00 to change the decimal to a percent. Sentence: 59 MHR Chapter : Probability

9 Working Example : Determine Probabilities From a Table You roll two 6-sided dice; is white and is grey. a) Make a table to show the sample space. Solution Complete the table to show all the possible combinations. White Die Grey Die b) What is the probability of rolling a sum greater than 0? Write your answer as a fraction a decimal and a percent. Sum means add. Solution Add the numbers in each cell. A cell is box from the table. White Die Grey Die P (sum > 0) How many cells add to more than 0? > means greater than C The probability of a sum greater than 0 is 0. or 8.%. 6. Determining Probabilities Using Tree Diagrams and Tables MHR 59

10 c) What is the probability that the number on the white die is larger than the number on the grey die? Write your answer as a fraction a decimal and a percent. Solution In the table shade all the outcomes where the white die number is larger than the grey die number. White Die Grey Die P (white die number larger than grey die) 6 C The probability of the white die number being number larger than the grey die number is 0. or %. 59 MHR Chapter : Probability

11 You spin the spinner and roll a 6-sided die. a) Complete the table to show the sample space. Spinner Die 5 6 b) What is P( )? P () decimal percent c) What is P(sum > 5)? Spinner > means greater than. Die P (sum >5) decimal percent. Determining Probabilities Using Tree Diagrams and Tables MHR 595

12 . John flips a coin and rolls a 6-sided die. a) What does P(H ) mean? b) John starts to draw a tree diagram to find the probability of flipping heads and rolling a. Explain what John has to do next to complete his tree diagram. Coin H Outcomes T. Monique missed class today. a) Explain how to use the table to show the sample space when you flip coins. Coin Heads Tails Coin Heads Tails b) What does favourable outcome mean? Give example using the table. 596 MHR Chapter : Probability

13 . Damien flips a coin and spins the spinner. a) Complete the tree diagram to show the sample space. Coin Spinner Outcomes H H T T b) List the sample space. ( ) ( ) c) What is the P(H )? Write your answer as a fraction a decimal and a percent. P(H ) 6 decimal percent d) What is P(T odd number)? Write your answer as a fraction a decimal and a percent. P(T odd number) Odd numbers end in 5 decimal percent. Determining Probabilities Using Tree Diagrams and Tables MHR 597

14 . Ali chooses card and rolls a 6-sided die. a) Complete the table to show the sample space Die 5 6 Cards 5 b) What is the probability that both numbers are the same? Write your answer as a fraction a decimal and a percent. P(both same number) decimal percent c) What is the probability that the sum of the die and the card is equal to 6? Write your answer as a fraction a decimal and a percent. P(sum is 6) decimal percent d) What is the probability that the number on the die is larger than the number on the card? Write your answer as a fraction a decimal and a percent. P(larger number on die) 598 MHR Chapter : Probability decimal percent

15 5. Lucy is fishing. She has an equal chance of catching a whitefish a trout an arctic char or losing a fish off the hook. What might she catch if she pulls her hook out twice? a) Complete the table to show all the possible combinations. Second Catch Whitefish (W) First Catch Trout (T) There are possible combinations. b) What is the probability she will catch arctic char: P(char char)? Sentence: c) What is P(whitefish char) in either order? Sentence: d) What is the probability she will catch nothing at all? Sentence:. Determining Probabilities Using Tree Diagrams and Tables MHR 599

16 6. You spin the spinner twice. a) Complete the tree diagram to show the sample space. T N E st Spin nd Spin Outcomes E N E N E E E E E E E E E T E T E There are. b) What is the probability of spinning E s? Sentence: c) What is P(same letter on both spins)? Sentence: 600 MHR Chapter : Probability

17 A game uses sticks. One side is bare and the other side is decorated. Toss the sticks in the air. They will land either decorated side up or bare side up. Your score depends on the number of times the decorated side lands face up. a) Complete the tree diagram to find all the when you toss sticks. Stick Stick Stick Stick Possible Outcomes b b b d b b b b b bare d decorated d d b d b) What is the probability that exactly sticks will land decorated side up? P(d d d) The probability of sticks landing decorated side up is.. Math Link MHR 60

18 . Warm Up. List the of each event. a) rolling a 6-sided die b) flipping a coin C A c) spinning this spinner. How many are there? a) rolling a -sided die b) choosing a card c) spinning this spinner 5 d) choosing a marble. Multiply. a) 5 8 b) 6 0 c) d) 7. Find the total value of each combination of coins. a) a quarter a dime and a nickel b) a loonie a quarter and a penny c) a dime a nickel a loonie and a penny 60 MHR Chapter : Probability

19 . Outcomes of Independent Events Working Example : Determine the Total Number of Outcomes From Two Events Carrie flips a coin and rolls a 6-sided die. How many are there? Solution Method : Create a Table Complete the table. Coin Flip There are Number on Die 5 6 H (head) H H T (tail) T T. Method : Use Multiplication Total number of on die on coin There are. The sandwich choices at the cafeteria are egg salad (E) or turkey (T). You can have white (W) rye (R) or brown () bread. Show ways to find the total number of. Create a Table: Types of read Sandwich Filling There are. Use Multiplication: Total number of number of different fillings number of types of bread There are.. Outcomes of Independent Events MHR 60

20 Working Example : Determine the Total Number of Outcomes From Three or More Events You flip a coin spin the spinner and roll a -sided die. a) How many are there? CENT A Solution C Method : Use a Tree Diagram Coin Head (H) Tail (T) Spinner A C Die Outcomes: The tree diagram shows Method : Use Multiplication Number of for. This row tells you the number of possible outcomes. a coin: the spinner: a -sided die: Total for coin for spinner for die There are. b) Why would it be difficult to show the sample space for this experiment in a table? Solution You can use a table for events. You can show event in the columns and event in the. For events you would need more than table to show all of the outcomes. 60 MHR Chapter : Probability

21 You are going to buy your lunch at school. You can choose of each of the following: sandwich: cheese or chicken fruit: orange apple or banana drink: juice water or milk How many different possible combinations are there? Show your answer ways. Use a Tree Diagram: Sandwich Fruit Drink Outcome Sentence: Use Multiplication: Total Sentence:. Outcomes of Independent Events MHR 605

22 . Jasmine has 5 tiles numbered from to 5 and a coin. She chooses tile and flips the coin. What are all the? 5 a) Use different methods to show how to find the number of. Tree Diagram: Table: Tiles Coins Multiplication: b) Which method do you like best? Give reason for your answer.. Explain why you cannot use table to find the when you have or more events. Use an example to help you explain your answer. 606 MHR Chapter : Probability

23 . A bag holds marbles red green and blue. A spinner has equal sections labelled and. You choose a marble and spin the spinner. a) Complete the table to show the sample space. G R Marbles Red (R) Green (G) lue () Spinner b) How many does the table show? c) Write a multiplication statement to show the outcomes. There are.. Flip a coin and choose a card. a) Complete the table to show all the Cards 5 Coin Heads (H) Tails ( ) There are. b) Use multiplication to check the number of. There are.. Outcomes of Independent Events MHR 607

24 5. You flip a coin roll a -sided die and choose a marble from a bag. Show the number of different ways. Tree Diagram: Coin Marble Die Outcome Multiplication: There are. 6. You have a nickel a dime and a loonie in your left pocket and a penny and a quarter in your right pocket. a) If you choose coin from each pocket how many different combinations could you get? Right Pocket Penny (P) Quarter (Q) Left Pocket Nickel (N) Dime (D) Loonie (L) Sentence: b) You choose coin from each pocket. What is the largest sum of money you could get? Sentence: 608 MHR Chapter : Probability

25 7. Tony has pairs of jeans and shirts. How many different combinations can he wear? Show your work. Draw a chart or tree diagram or use the multiplication method. 8. The birthday menu at the lue ird Restaurant gives you choice from each category: Drinks: choices Meal: choices Dessert: choices How many possible combinations are there? Show your work. In the stick game each stick can land decorated or bare side up. a) Find the total number of when you toss sticks. Use multiplication. Each stick has sides or. Stick Stick Stick Stick total (possible (possible (possible (possible outcomes) outcomes) outcomes) outcomes) b) If you used 5 sticks how many would there be?. Math Link MHR 609

26 Name:. Warm Up. Erv flips a coin and rolls a 6-sided die. Show the sample space using a tree diagram. Coin Heads Tails Die Outcomes. Multiply the fractions. Example: 6 a) b) 7. Change the fractions to decimals. 9 a) b) 0 5. Circle the decimal that has a larger value. a) 0.5 or 0. Think about money! b). or.0 60 MHR Chapter : Probability

27 . Determining Probabilities Using Fractions Working Example : Calculating Probabilities Using a Table and Multiplication Mackenzie spins a spinner and rolls a -sided die. a) Complete the table to show the sample space. How many are there? Solution Die Spinner lue () b) What is P( )? Write your answer as a fraction. Solution Shade the cells that have a and a. P ( ) yellow red blue Red (R) Yellow(Y) Number of :. c) Use multiplication to find P(blue ). The probability of getting blue and is. Solution Find each probability separately. number of blue sections on spinner P () total number of sections on spinner P () number of s on die number of sides on die Multiply the probabilities of the single events. ( ) ( ) P(blue ) P P. Determining Probabilities Using Fractions MHR 6

28 Name: d) Using the information in the table what is P(red or blue )? Write your answer as a fraction. Die Spinner lue () Red (R) R R R R Yellow(Y) Y Y Y Y Solution In the table circle (R ) and ( ). P(R or ) e) Use multiplication to check your answer in part d). Solution yellow red blue P (R or ) P () Multiply the probabilities of the events. P(R or ) P() 6 MHR Chapter : Probability

29 You roll a -sided die and spin the spinner. Find the probability of rolling a number less than and spinning A. Check your answer using multiplication. Complete the table. A Die Spinner A P (number less than and A) Check using multiplication. A P (number less than ) P (A) P(number less than ) P(A). Determining Probabilities Using Fractions MHR 6

30 Name: Working Example : Calculating Probabilities Using a Tree Diagram and Multiplication Jason rolls a -sided die and spins the spinner. What is the probability of rolling an even number and spinning a? Show your answer using a tree diagram and multiplication. Solution Tree Diagram: A C Die Spinner Outcomes There are. A C A C There are favourable outcomes (look for even numbers with s). Even numbers end in 0 6 P (even number and ) Multiplication: Die: P (even number) Spinner: P () P(even number ) P(even number) P() 6 MHR Chapter : Probability oth methods give the same result.

31 You roll a -sided die and spin the spinner. Find the probability of rolling a and spinning. Check your answer using multiplication. Tree diagram: A Die Spinner A Outcomes A P ( ) Multiplication: Die: P () Spinner: P () P() P(). Determining Probabilities Using Fractions MHR 65

32 Name: Working Example : Simulations simulation using an experiment instead of a real situation Gina uses a simulation to show the probability that both traffic lights will be red on her way to soccer practice. a) What is the experimental probability that both lights are red? Write your answer as a fraction a decimal and a percent. red green red green red experimental probability the chance of an event occurring based on the results of an experiment number of experimental probability number of trials Solution Gina records her results from spinning the spinner twice. Complete the chart. Results From Experiment Trial First Light (Green or Red) Second Light (Green or Red) oth Lights Red? (yes or no) R R yes G G no R G G R 5 R R 6 R G 7 R R 8 G G 9 G R 0 G G The chart shows. How many are yes? P(both lights red) 0 The experimental probability that both lights are red is 0. or %. 66 MHR Chapter : Probability

33 b) What is the theoretical probability that both lights are red? theoretical probability the calculated chance that an event will occur number of theoretical probability total number of example: the probability of tossing heads on a coin is Solution The probability that light will be red on the spinner is 5. P(both lights red) P(first light red) P(second light red) 5 5 red green red green red decimal The theoretical probability that both lights are red is 0. or %. c) Compare the experimental and theoretical probabilities. Solution These probabilities are close but not exactly the same. The experimental probability is (higher or lower) than the theoretical probability. If Gina did the experiment more times the experimental and theoretical probabilities would likely be closer.. Determining Probabilities Using Fractions MHR 67

34 Name: Andrew flips coins 00 times to show the chance of having a boy or girl in a family with children. Heads means a girl and tails means a boy. The table shows the results of his experiment. Coin Outcomes HH HT TH TT Child outcomes girls girl boy boy girl boys Number of results 7 7 a) Look at the table. What is the experimental probability of getting boys? number of experimental probability number of trials P( boys) The experimental probability of getting boys is 0. or %. b) What is the theoretical probability of getting boys? P( boys) P(T on first coin) P(T on second coin) A coin has outcomes. The theoretical probability of getting boys is 0. or %. 68 MHR Chapter : Probability

35 . A bag holds black white and grey marble. Another bag holds penny and dime. Explain how to use multiplication to find the probability of choosing grey marble and penny [P(grey and penny)]. CENT. Describe what a simulation is. Give an example of when you could use a simulation.. rittany spins the spinner and rolls a -sided die. a) Complete the table to show the sample space. D A C Die Spinner A C D b) What is P( A)? P ( A) c) Use multiplication to find P( A). P( A) P() P( ). Determining Probabilities Using Fractions MHR 69

36 Name:. You flip a coin twice. a) Complete the tree diagram to show the sample space. First flip Second flip Outcomes b) What is P(H H)? P( ) c) Check your answer using multiplication. P(H H) P( ) P( ) 5. Grade 8 students are planting types of flowers: daisy (D) marigold (M) rose (R) and tulip (T). The students can plant them in places: school (S) flowerpot (F) park (P) and hospital (H). Tamira does an experiment to see where the different flowers will be planted. The sample space is (M F) (R H) (D S) (M F) (T H) (T P) (D H) (R P) (M P) (R F). a) What is the experimental probability of getting P(marigold flowerpot)? P(M F) number of 0 number of trials b) Use multiplication to find the theoretical probability of P(marigold flowerpot). P(marigold) P(flowerpot) P(marigold flowerpot) P(marigold) P(flowerpot) 60 MHR Chapter : Probability

37 6. Josh is ordering pizza for his soccer team. There are specials: Peppy Pepperoni Happy Hawaiian and Cheery Cheese. He can choose from types of crust: regular or thin. a) How many different combinations of pizza are there? Show your thinking. Sentence: b) What is the probability he will choose Happy Hawaiian with thin crust? Use different ways to show your answer. c) Josh finds out of the players is allergic to pepperoni. How many combinations of pizza are there without pepperoni? Sentence:. Determining Probabilities Using Fractions MHR 6

38 Name: 7. a) Complete the tree diagram to find the outcomes for spinners. b) Draw a picture of each spinner. Spinner Spinner Outcome A A c) What is P(A )? Sentence: 8. The weather forecaster predicts that there is a 70% chance of rain in Victoria and a 0% chance of rain in Calgary. What is the probability that it will rain in both cities? 70% is the same as or % 00 0 P(rain in Victoria rain in Calgary) P(Victoria) P(Calgary) Sentence: 6 MHR Chapter : Probability

39 You toss sticks. a) What is the theoretical probability that all of them land decorated side up? P(decorated decorated decorated) P(decorated) P(decorated) P(decorated). P( ) b) Create a simulation to find the experimental probability of sticks landing decorated side up. Step : Use a coin because it has. Step : Do 0 or more trials. Step : Draw a chart to record your results. Use the headings below. Let heads represent the decorated side and tails represent the bare side. Trials Stick (First toss) Stick (Second toss) Stick (Third Toss) All Three Decorated Side Up? (yes or no) Step : What is the experimental probability that all sticks landed decorated side up? P( ) total number of trials c) Compare the experimental and theoretical probabilities.. Math Link MHR 6

40 Name: Chapter Review Key Words For # to #5 unscramble the letters. Use the clues to help you.. ENITPDENEDN TSVEEN or more events that do not affect each other ( words). MELAPS PEACS all the of an event ( words). ONMISULIAT an experiment used instead of trying to re-create the real situation. YPORTLIIA the chance of an event happening 5. VFAEALOUR CMOETUO what you want to happen ( words). Determining Probabilities Using Tree Diagrams and Tables pages Leah rolls two 6-sided dice. a) Complete the table to show the sample space. Die Die b) What is the probability that the numbers are the same? c) What is the probability that the sum of the numbers is 0? P( numbers the same) P(sum is 0) 6 MHR Chapter : Probability

41 7. You flip a coin times. a) Complete the tree diagram to show the sample space. Flip # Flip # Flip # Outcome H H T T H T b) What is the probability that all flips will be heads? c) What is the probability of flipping exactly heads and tail in any order? P(H H H). Outcomes of Independent Events pages You flip a coin and spin the spinner. a) Use a table to find the total number of. Spinner Coin The total number of is. b) Use multiplication to check your answer. Total for coin for spinner Chapter Review MHR 65

42 Name: 9. Janessa wins a contest on the radio. She can choose item from each category for her prize package: T-shirt choices CD choices concert ticket choices How many different packages can she choose from? Show your work. Total shirt Sentence:. Determining Probabilities Using Fractions pages There are bags of marbles. One bag has black marbles and grey marbles. The other bag has white marbles and grey marble. You choose marble from each bag. a) What is the probability that you will choose a black marble? P(black marble) number of black marbles total number of marbles in bag b) What is the probability that you will choose a white marble? P(white marble) c) What is P(black marble white marble)? P(black marble white marble) P(black marble) P(white marble) 66 MHR Chapter : Probability

43 . You roll a 6-sided die times. Use multiplication to find the probability of rolling even numbers. How many even numbers are on a die? How many are there on each die? P( even numbers) P(even) P(even) P(even) Sentence:. You spin the spinner 0 times. The table shows the results. Red Purple Green lue 5 8 a) What is the theoretical probability of the spinner landing on blue? Write your answer as a decimal. lue Green Red Purple number of blues on spinner P (blue) total number of colours on spinner decimal b) Look at the chart. What is the experimental probability of the spinner landing on blue? Write your answer as a decimal. P (blue) number of number of trials total number of spins decimal c) Why are the answers to parts a) and b) different? Chapter Review MHR 67

44 Name: Practice Test For # to # circle the correct answer. You roll two -sided dice. The table shows the sample space for the. Use the table to answer # to #.. What is the probability that the same number is on each die? 8 A 6 6 C D 6 6 Die Die. What is the probability that the sum of both numbers is 6? A C D 6 6 Sum is the answer when you add.. What is the probability that neither die has a showing? 7 A C D 6 6 For # and #5 fill in the blanks using the coin and spinner.. The total number of is (coin possible (spinner possible (total possible outcomes) outcomes) outcomes) M R O A D N 5. To find the probability of the coin landing heads up and the spinner landing on A multiply and. P(H) and P(A). 68 MHR Chapter : Probability

45 Short Answer 6. a) What is the total number of possibilities if you choose drink meal and dessert from the menu? Show your work. CAFETERIA Drink choices: milk apple juice Meal choices: burger pizza chicken strips Dessert: ice cream chocolate cake fresh fruit Sentence: b) What is the probability that you would choose milk chicken strips and ice cream? Sentence: 7. A bag has black marbles and white marbles. A jar has striped jellybean and grey jellybeans. You choose marble and jellybean. a) What is the probability of choosing a striped jellybean? Sentence: b) What is the probability of choosing a black marble and a grey jellybean? Sentence: Practice Test MHR 69

46 Name: 8. David wants to see who the students will vote for in the next school election. He decides to survey the next 0 people who walk into the library. The table shows his results. Candidates Jesse Maria Marcus Angela Votes 7 8 a) What is the experimental probability that students will vote for Maria? Write your answer as a fraction a decimal and a percent. Number of Number of P(votes for Maria) Sentence: b) What is the experimental probability that students will vote for either Marcus or Angela? Number of Number of P(votes for Marcus or Angela) Sentence: 60 MHR Chapter : Probability

47 a) Make a set of sticks for a stick game. Decorate side of each stick. b) Play the stick game. With a partner take turns dropping all sticks at once. Use the table to find the score of each drop. Play until person reaches a score of 50. Record your results for each toss and keep a running score in the chart. Me Decorated Sides Up Score Partner Decorated Sides Up Score decorated sides up 5 points decorated sides up points decorated sides up point decorated side up points 0 decorated sides up 5 points c) Use the tree diagram you made for the Math Link on page 60. Find the theoretical probability for each of the following: P( decorated sides up) P( decorated sides up) P( decorated sides up) P( decorated side up) P(0 decorated sides up) d) Do you think the scoring system is fair? Give reason for your answer. Practice Test MHR 6

48 Name: Use the clues to fill in the blanks. Then complete the crossword puzzle. Across 5. The includes all the possible outcomes of an event. ( words) 6. The outcome you want to happen is called the. ( words) 7. do not affect the results of the other event. ( words) Down. The chance of an event happening is called.. When you use an experiment to predict the probability of something happening it is called probability.. probability is what should happen all of the time.. You can use a to model the real situation MHR Chapter : Probability

49 Math Games Play Fair! A fair game means each player has an equal chance of winning the game. There are games described below. Play each game with a partner to see if each game is fair. two 6-sided dice coin per pair of students Tally Charts LM Game Rules Flip a coin. Heads is Player A and tails is Player. Player goes first. Taking turns roll dice and add the values Player A scores a point for each even total he or she rolls. Player scores a point for each odd total he or she rolls. The first player to reach 0 points wins. Use a tally chart to keep track of your score. Who won? Player Game Rules Repeat Game except Player A scores a point for every total that is 7 or less. Player scores a point for each total that is 8 or more. Use a tally chart to keep track of your score. Who won? Player Which game do you think is not fair? Circle GAME or GAME. The table shows the sum of die. Use the table to find the probability of winning each game. Die Die Game Player A: P(even total) Game 6 Player : P(odd total) 6 Player A: P(7 or less) Player : P(8 or higher) 6 6 Which game is fair (both players have an equal chance of winning)? Explain how you know. Math Games MHR 6

50 Name: Challenge in Real Life Treasure Hunt A group of treasure hunters found a map. The map shows treasure in an area that is 0 km by 0 km. It is divided into zones. coloured pencils Zone Zone Zone Zone You be the treasure hunter. What are your chances of finding treasure?. Use colours as clues on your map. yellow is treasure white is ice brown is sand There are 00 squares on the map. The ratio of yellow squares : white squares : brown squares is : 5 :. Show this ratio on the grid. Multiply each ratio by 0 to find the number of squares to colour. 0 : 5 0 : 0 : : for 00 squares. Yellow: White: squares squares rown: squares Use your answers to randomly colour the right number of squares. Use the correct colour. 6 MHR Chapter : Probability

51 . What is the theoretical probability of each colour on the map? P(yellow) 00 P(white) 00 P(brown) 00. What is the theoretical probability of choosing each zone in the grid? P(Zone ) 00 P(Zone ) 00 P(Zone ) 00 P(Zone ) 00. You only have time to search zones for the treasure. Which zones will you search? Explain why you chose each zone. Zone Which zones will let you cover the most ground? Zone 5. Do you have a good chance of finding the treasures in the zones you chose? Circle YES or NO. Give reason for your answer. Challenge in Real Life MHR 65

52 Answers Get Ready pages a) 0.5;.5% b) 0.75; 75% %. a) Die Spinner 5 6 A A A A A A 5 A b) (A ) (A ) (A ) (A ) (A 5) (A 6) ( ) ( ) ( ) ( ) ( 5) ( 6) Math Link Answers will vary. Examples: a) Go Fish b) YES c) You have to get pairs of the same card. d) Monopoly e)yes f) You roll the dice to see how many places you move on the board. g) Answers will vary.. Warm Up page 589. a) 0. ;. % b) 0.6 ; 66.6 % c) 0.7; 77.7 % d) 0.7; 7.7 %. a) 6 ; 0.6 b) 6 ; 0.5. a) 0.5 b) 0.5 c) 0. d) 0.. Determining Probabilities Using Tree Diagrams and Tables pages Working Example : Show You Know a) Coin Die Outcomes H H H H H T T T T T b) 8 c) P(H ) is 0.5 or.5%. 8 Working Example : Show You Know a) Die Spinner b) P( ) is 0.06 or.6 %. c) P(sum > 5) is or 58. %. Communicate the Ideas. Answers may vary. Example: a) P(H ) means the probability of flipping a head and rolling a. b) John has to label Die on the tree diagram next.. Answers may vary. Example: a) Write the choice from the row and column in each cell of the table. b) A favourable outcome is a successful result in an experiment. If you want heads (H H) is a favourable outcome. Practise. a) Coin Spinner Outcomes b) (H ) (H ) (H ) (T ) (T ) (T ) H H T H H T T T c) P(H ) or 6.6 % d) P(T odd number) 0. or. % 6. a) Die Cards b) P(both same number) 0.6 or 6.6 %. 8 c) P(sum is 6) 0.6 or 6.6 %. 8 d) P(larger number on die) Apply 5. a) First Catch 6 0. or. % 8 Whitefish (W) Second Catch Trout (T) Arctic Char (A) Losing a Fish (L) Whitefish (W) W W W T W A W L Trout (T) T W T T T A T L Arctic Char (A) A W A T A A A L Losing a Fish (L) L W L T L A L L There are 6. b) P(char char) % 6 c) P(whitefish char) 0.5.5% 8 d) P(catch nothing) 6. a) st Spin N E E T nd Spin N E E T N E E T N E E T N E E T % 6 Outcomes N N N E N E N T E N E E E E E T E N E E E E E T T N T E T E T T There are 6. b) P(spinning E s) 0.5 5% 6 c) P(Same letter on both spins) % 6 66 MHR Chapter : Probability

53 Math Link a) b) Stick Stick Stick Stick Possible Outcomes bare decorated 6. Warm Up page 60. a) 5 6 b) heads tails c) A C. a) b) 5 c) 5 d). a) 0 b) 60 c) 8 d). a) 0 b) $.6 c) $.6. Outcomes of Independent Events pages Working Example : Show You Know Types of read White (W) Rye (R) rown () Sandwich Egg Salad (E) E W E R E Filling Turkey (T) T W T R T There are 6. Working Example : Show You Know Sandwich Fruit Drink Outcome Juice Cheese Orange Juice Orange Water Cheese Orange Water Milk Cheese Orange Milk Cheese Chicken Apple anana Orange Apple anana bare decorated bare decorated Juice Water Milk Juice Water Milk Juice Water Milk Juice Water Milk Juice Water Milk There are 8. bare decorated bare decorated bare decorated bare decorated Cheese Apple Juice Cheese Apple Water Cheese Apple Milk Cheese anana Juice Cheese anana Water Cheese anana Milk Chicken Orange Juice Chicken Orange Water Chicken Orange Milk Chicken Apple Juice Chicken Apple Water Chicken Apple Milk Chicken anana Juice Chicken anana Water Chicken anana Milk bare decorated bare decorated bare decorated bare decorated bare decorated bare decorated bare decorated bare decorated b b b b b b b d b b d b b b d d b d b b b d b d b d d b b d d d d b b b d b b d d b d b d b d d d d b b d d b d d d d b d d d d Communicate the Ideas. a) Coin Tiles Outcomes H H Heads H H 5 H 5 Coin Tiles 5 Heads (H) H H H H H 5 Tails (T) T T T T T There are 0. b) Answers will vary.. Answers may vary. Example: You can only compare things in table because you can use rows for one and columns for the other.. a) Spinner Red (R) R R R Marbles Green (G) G G G lue (). a) 5. b) 9 c) 9 Coin Tails Cards Heads (H) H 5 H 6 H 7 H 8 H 9 H 0 Tails (T) T 5 T 6 T 7 T 8 T 9 T 0 There are. b) 6 Coin H T 6 Apply 6. a) 6 b) $ Math Link a) 6 b) 5 Marble lack White lack White T T T T T 5 Die Outcome H lack H lack H lack H lack H White H White H White H White Tails lack Tails lack Tails lack Tails lack Tails White Tails White Tails White Tails White Answers MHR 67

54 . Warm Up page 60. Coin Die Outcomes H H H Heads H 5 H 5 6 H 6. a) 8 b). a) 0. b) 0.6. a) 0.5 b).. Determining Probabilities Using Fractions pages 6 6 Working Example : Show You Know Die Spinner A A A A A P(numbers less than and A) 8 Working Example : Show You Know Die Spinner Outcomes A A Tails A A A 5 6 T T T T T 5 T 6 A A A P( ) 8 Working Example : Show You Know a) % b) 0.5 5% Communicate the Ideas. Answers may vary. Example: Multiply the probability of selecting a grey marble by the probability of selecting a penny.. Answers may vary. Example: A simulation is when you use an experiment to model a real situation. You might use a simulation of flipping coins to model the probability of it raining one day. Practise. a) Spinner Die A C D A C D A C D A C D A C D. a) b) P(H H) c) P(H H) 5. a) P(marigold flowerpot) Apply 6. a) 6 b) % c) 6 7. a) First flip Second flip Outcomes Spinner Spinner Outcomes A A A A A A H T 0 b) P(marigold flowerpot) 6 A A A A b) c) P(A ) A A % or % 00 Math Link a) 8 b) and c) Answers will vary. Chapter Review pages independent events. sample space. simulation. probability 5. favourable outcome 6. a) Die Die b) P( numbers the same) c) P(sum is 0) H T H T 6 or H H H T T H T T 6 6 or 6 b) P( A) 6 c) P( A) 6 68 MHR Chapter : Probability

55 7. a) Flip # Flip # Flip # Outcomes H H H H H T H H T 8. a) H T b) P(H H H) 8 c) 8 Coin Spinner H H H H T T T T The total number of is 6. b) 6 9. packages T H T 0. a) P(black marble) 5 b) P(white marble) 5 H T H T H T c) P(black marble white marble) 5 7. P( even numbers) 6 or 8. a) P(blue) 0.5 b) P(blue) 0.5 c) Answers may vary. Example: The experimental probability is based on an experiment but the theoretical probability is based on what should happen. Practice Test pages C. D H T H H T T T H H T H T T T H T T T Wrap It Up! page 6 a) and b) Answers will vary. c) P( decorated sides up) P( decorated sides up) 6 P( decorated sides up) P( decorated sides up) 6 P(0 decorated sides up) d) Answers will vary. Example: Yes 6 because you get more points for combinations that are less probable. Key Word uilder page 6 Across 5. sample space 6. favourable outcome 7. independent events Down. probability. experimental. theoretical. simulation Math Games page 6 P(even total) 8 6 P(odd total) 8 6 P(7 or less) 6 P(8 or higher) 5 6 Challenge in Real Life pages yellow: 0 squares white: 50 squares brown: 0 squares. P(yellow). P(Zone ) P(Zone ) 00. Answers will vary. 5. Answers will vary P(white) 50 0 P(brown) P(Zone ) 8 8 P(Zone ) a) 8 b) 8 7. a) b) a) 7 0. or. % b) 0. or 0% 0 0 Answers MHR 69

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