Probability Grade 10 Third Quarter Lessons

Grade 10

1. QUARTER 3 WEEK 7

2. OBJECTIVES: Differentiate experimental probability from theoretical probability. Determine the probability of an event E of a. experimental probability. b. theoretical probability.

3. Let’s Recall! Experiment A process by which an observation is obtained. Trial (No. of Trials) One instance of an experiment (the number of times an experiment is repeated). Outcome An observed result of an experiment. Sample Space The set of all possible outcomes of an experiment. Event A set whose elements are some outcomes of an experiment (a subset of the sample space). Random Experiment a process that can be repeated under similar conditions but whose outcome cannot be predicted with certainty beforehand. Sample Point An element of a sample space.

4. Review: How many outcomes are there in the sample space of each experiment below? 1. Rolling 2 dice. 2. Tossing 3 coins. 3. Rolling a die and tossing a coin. 4. Drawing a ball from a bowl containing 2 green balls, 5 red balls, and 7 yellow balls. 5. Selecting a representative from a class of 40 students. n(S) = 36 n(S) = 8 n(S) = 12 n(S) = 14 n(S) = 40

5. Review: How many outcomes are there in the sample space of each experiment below? 6. Arranging the letters of the word SATURN. 7. Arranging 5 students around a campfire. 8. Electing president, vice president, and secretary in a class of 30 students. 9. Selecting 5 members to form a committee from 20 teachers. 10. Forming a committee of 5 members from 12 girls and 8 boys. n(S) = 720 n(S) = 24 n(S) = 24,360 n(S) = 15,504 Sol’n: 6! Sol’n: (5-1)! = 4! Sol’n: 30 P 3 Sol’n: 20 C 5 n(S) = 15,504 Sol’n: 20 C 5

6. Review: How many outcomes are there in each event given an experiment? 1. Rolling 2 dice ang getting a sum of 7. 2. Tossing 3 coins and 2 heads appear. 3. Getting a prime number and a head when a die is rolled and a coin is tossed. 4. Drawing a blue ball from a bowl containing 2 green balls, 5 red balls, and 7 yellow balls. 5. Drawing a face card from a standard deck of 52 cards. n(E) = 6 n(E) = 3 n(E) = 3 n(E) = 0 n(E) = 12

7. Review: How many outcomes are there in each event given an experiment? 6. Cases that start with a vowel when the letters of the word SATURN are arranged. 7. Arrangements with 2 particular students always seated together when 5 students are seated around a campfire. 8. Electing Amy as the president during the election of president, vice president, and secretary in a class of 30. 9. Choosing Miss Cruz to be part of the committee of 5 members from 20 teachers. 10. Forming a committee of 5 members consisting 3 girls and 2 boys from 12 girls and 8 boys. n(E) = 240 n(E) = 12 n(E) = 812 n(E) = 3,876     Sol’n: 29 P 2 Sol’n: 19 C 4 n(E) = 6,160 Sol’n: 12 C 3 • 8 C 2

8. Motivation Probability measures the likelihood or chance that an event will occur. What is the probability that you will be joining the forthcoming JS Promenade? During basketball practice, Zach shoots 7 balls out of 13 tries. What is the probability that Zach will shoot the next ball? What is the probability of choosing a heart suit card in a standard deck of cards?

9. One more term … Probability Measures the likelihood or chance that an event will occur Can be expressed in Fractions, Decimals, or Percentage

10. How do we describe the likelihood of an event without using numerical values?

11. The Likelihood Scale Impossible Unlikely 50% Chance Likely Certain finding a person capable of running 2000km per second the event that it rains in summer getting a head when tossing an unbiased coin getting a number higher than 2 when an unbiased die is tossed drawing a red marble from an urn containing 4 red marbles

12. The Likelihood Scale Impossible Unlikely 50% Chance Likely Certain finding a person capable of running 2000km per second the event that it rains in summer getting a head when tossing an unbiased coin getting a number higher than 2 when an unbiased die is tossed drawing a red marble from an urn containing 4 red marbles

13. The Likelihood Scale Impossible Unlikely 50% Chance Likely Certain the event that you will become the president of the Philippines this coming election the day after Thursday is Friday the date after the 29 th is the 30 th in a month the event that you will drink water sometime during the day someone from this class will be sick tomorrow

14. The Likelihood Scale Impossible Unlikely 50% Chance Likely Certain the event that you will become the president of the Philippines this coming election the day after Thursday is Friday the date after the 29 th is the 30 th in a month the event that you will drink water sometime during the day someone from this class will be sick tomorrow

15. Theoretical vs. Experimental Probability THEORETICAL PROBABILITY -The probability is determined even before the experiment is performed. -The theoretical probability of event E is the ratio of the number of outcomes in E to the total number of outcomes in the sample space S , assuming all outcomes are equally likely. Classical / A priori Probability

16. Theoretical vs. Experimental Probability THEORETICAL PROBABILITY Classical / A priori Probability  

17. Theoretical vs. Experimental Probability EXPERIMENTAL PROBABILITY -The probability is determined by repeating the experiment a large number of times. -As the number of repetitions of an experiment increases, Empirical Probability of E → Theoretical Probability of E Empirical / A posteriori Probability

18. Theoretical vs. Experimental Probability EXPERIMENTAL PROBABILITY Empirical / A Posteriori Probability  

19. EXAMPLES Identify whether the following situations involve theoretical or experimental probability then solve its probability . 1. During a basketball practice, Zach shoots 7 balls out of 13 tries. What is the probability that Zach will shoot the next ball? Experimental Probability The experiment is repeated several times and the probability of the next shoot will be based on the previous trials. There are 13 trials, so n(S) = 13. Zach made 7 shots (favorable outcomes), n(E) = 7.  

20. EXAMPLES Identify whether the following situations involve theoretical or experimental probability then solve its probability . Theoretical Probability No trials are made yet. The probability is to be determined even before the experiment. There are 52 cards in a deck, so n(S) = 52. There are 13 cards in a heart suit, so n(E) = 13.   2. What is the probability of choosing a heart suit card in a standard deck of cards?

21. 3. A die is tossed 100 times. The following outcomes were recorded in the table below. Based on this table what is the probability that the die will have an outcome of 5? Outcomes 1 2 3 4 5 6 No. of times appeared 25 25 15 20 10 5 EXAMPLES Experimental Probability Identify whether the following situations involve theoretical or experimental probability then solve its probability .

22. Outcomes 1 2 3 4 5 6 No. of times appeared 25 25 15 20 10 5 10 What is P(5)? 100 1 10 EXAMPLES P(5) = P(5) =

23. EXAMPLES 4. Out of 840 spins, about how many times should the arrow is expected to land on the white sector? Identify whether the following situations involve theoretical or experimental probability then solve its probability . Theoretical Probability The probability that the arrow will land on the white sector is:    

24. PRACTICE EXERCISE 1. What is the theoretical probability that violet will occur? 2. What is the experimental probability that yellow will occur on the next spin? 3. What is the theoretical probability that blue will occur? 4. What is the experimental probability that blue will occur on the next spin? 5. What is the theoretical probability that red will occur?          

25. Generalization 1. How are experimental and theoretical probability applied in real life? 2. Differentiate theoretical probability from experimental probability. 3. How do we determine the probability of an event E of a. experimental probability? b. theoretical probability?

26. EVALUATION: 1. In the last 20 days of April, it rained 3 times in Metro Manila. What is the probability that it will rain tomorrow in Metro Manila? 2. A die is rolled, find the probability of getting an even number. 3. In a class of 40 students, 12 have birthdays on any month from January to March, 8 students have birthdays on any month from April to June, and 9 from July to September. What is the probability that when a student is called, his/her birthday is on any month from October to December? 4. A card is drawn 10 times with replacement from a deck of 52 cards. Of the outcomes, 3 are face cards, 4 are number cards, and 3 are aces. What is the probability that the 11 th card will be a number card? Identify whether the following situations involve theoretical or experimental probability then solve its probability. .        

27. ADDITIONAL / ENRICHMENT ACTIVITY Watch the video https://www.mrmaisonet.com/probability/video/212-experimental-vs-theoretical-probability

28. Probability of Simple Events DAY 3

29. OBJECTIVES: Illustrate the probability of simple events. Solve problems involving the probability of simple events.

30. In the Philippine 6/49 lotto, a bet consists of choosing any 6 numbers in no particular order from 1 to 49. What is your chance of winning if you bet on three cards?

31. SIMPLE PROBABILITY In probability, we have to remember the following: The probability is a number from 0 to 1. The probability of a certain event is 1. The probability of the impossible event is 0. The sum of the probabilities of all the outcomes in the sample space is 1.  

32. SIMPLE PROBABILITY 1. When a die is rolled, find the probability of getting: a. a number greater than 3.        

33. SIMPLE PROBABILITY 1. When a die is rolled, find the probability of getting: b. a number greater than 6.   This is an example of an impossible event .

34. MORE ON PROBABILITY 2. Two dice are rolled. Find the probability of getting: a. a sum of 7. The event of getting a sum of 7:                    

35. MORE ON PROBABILITY 2. Two dice are rolled. Find the probability of getting: b. a double. Getting a double means the 2 dice show the same number.     We know that      

36. MORE ON PROBABILITY 2. Two dice are rolled. Find the probability of getting: c. a sum of less than 13. This is a certain event because the sum of all the pairs is ranging from 2 to 12. All their sums are less than 13.  

37. EXAMPLES 3. There are blue, red and green marbles in a jar. If there are 7 blue marbles, the probability of getting a blue marble is 1/6 and the probability of getting a red marble is 5/7 , then how many green marbles are there in the jar?       By MPE         By MPE     By APE   There are 5 green marbles in the jar.

38. MORE ON PROBABILITY Complement Rule If the probability that event A will happen is a, then the probability that event A will not happen is 1 – a.

39. EXAMPLES 1. If there is 15% chance of failing a certain test in Math, what is the probability of passing that test?  

40. EXAMPLES 2. If the probability that it will rain tomorrow is 0.20, what is the probability that it will not rain tomorrow?  

41. Activity 1: 1. A pencil case contains 3 pencils, 4 ballpens, and 5 colored pens. What is the probability that if one item is drawn at random, it is a pencil? 2. When a die is rolled, find the probability of getting: a. an odd number. b. a prime number. c. a number less than or equal to 3? 3. A card is drawn from a deck of 52 cards. What is the probability that it is: a. a face card? b. an ace? c. a black number card? d. not a red queen? e. a black diamond? Solve each problem accordingly. Simplify your answers.                  

42. Activity 1: 4. A shopping mall has set up a promotion as follows. With any mall purchase of P2500 or more, the customer gets to spin the wheel shown below. If a number 1 comes up, the customer wins P500. If the number 2 comes up, the customer wins P250; and if the number 3 or 4 comes up, the customer wins a discount coupon. Find the following probabilities. a. The customer wins P500. b. The customer wins P250. c. The customer wins money. d. The customer wins a coupon. Solve each problem accordingly. Simplify your answers.        

43. Activity 1: 5. There are 15 red cards, some blue cards and some white cards in a box. If the probability of drawing a blue card is 1/8 and the probability of drawing a white card is twice the probability of getting a blue card, how many cards are there in the box? Solve each problem accordingly. Simplify your answers.    

44. Generalization How do we determine the probability of event E? Give the range of values for a probability. What is the probability of a certain event? Impossible event? 5. What is the complement rule for probability?

45. EVALUATION

46. EVALUATION 1. Two dice are rolled. What is the probability that: a. the sum is less than 12? b. the sum is greater than 9? c. both are prime? d. both are even? e. have a sum of at least 7? 2. Spin the dial. What is the probability of: a. the event A that the pointer stops on white? b. the event B that the pointer stops on the green? c. the event C that the pointer stops on an even number? d. the event D that the pointer stops on an odd number? 3. Joe will spin the dial 320 times. About how many times should Joe expect to land on the violet sector? 4 . How many times can we expect to land on each prime number if we take 96 spins? 3 1 2 4 5 Figure for 6, 7, and 8.

47. EVALUATION 5. A certain class of 60 students was categorized by gender and by grade (passed, failed, or incomplete). The counts were: What is the probability that a student chosen from the class a. is a male? b. did not pass? c. is a female who passed? d. incomplete? e. is a male who failed? 6. A student has a 0.44 probability of passing the college entrance test. About how many students took the test if 205 passed? Passed Failed Incomplete Male 25 3 5 Female 20 4 3

48. Checking of Evaluation

49. INDEPENDENT PRACTICE 1.Two dice are rolled. What is the probability that: a. the sum is less than 12? b. the sum is greater than 9? c. both are prime? d. both are even? e. have a sum of at least 7? 2 . Spin the dial. What is the probability of: a. the event A that the pointer stops on white? b. the event B that the pointer stops on the green? c. the event C that the pointer stops on an even number? d. the event D that the pointer stops on an odd number? 3 . Joe will spin the dial 320 times. About how many times should Joe expect to land on the violet sector? 4 . How many times can we expect to land on each prime number if we take 96 spins?           3 1 2 4 5         7. 40 Figure for 6, 7, and 8. 8. 2, 24 times; 3, 12 times ; 5, 24 times

50. INDEPENDENT PRACTICE 9. A certain class of 60 students was categorized by gender and by grade (passed, failed, or incomplete). The counts were: What is the probability that a student chosen from the class a. is a male? b. did not pass? c. is a female who passed? d. incomplete? e. is a male who failed? 10. A college entrance test has a 0.44 probability of passing. About how many students took the test if 205 passed? Passed Failed Incomplete Male 25 3 5 Female 20 4 3           10. 466

51. DAY 4: PROBABILITY OF UNION OF TWO EVENTS

52. OBJECTIVES: differentiate mutually exclusive from non-mutually exclusive events; illustrate the probability of the union of two events; and solve problems involving the probability of the union of two or more events.

53. Choose the activities that can be performed simultaneously and those that cannot. D. A. B. C. E. F.

54. MUTUALLY AND NON-MUTUALLY EXCLUSIVE EVENTS

55. Consider the following pairs of events. Drawing a Queen Drawing an Ace Drawing a Diamond Drawing a Red Face Card

56. Consider the following pairs of events. Drawing a Queen Drawing an Ace Drawing a red suit Drawing a Face Card Q♦ Q♠ Q♥ Q♣ A♦ A♠ A♥ A♣ Drawing a Queen Drawing an Ace Drawing a Diamond Drawing a Red Face Card A♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦ J♦ Q♦ K♦ J♥ Q ♥ K♥

57. Consider the following pairs of events. Drawing a Queen Drawing an Ace Drawing a red suit Drawing a Face Card Q♦ Q♠ Q♥ Q♣ A♦ A♠ A♥ A♣ Drawing a Queen Drawing an Ace Drawing a Diamond Drawing a Red Face Card A♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦ J♥ Q ♥ K♥ MUTUALLY EXCLUSIVE EVENTS NON-MUTUALLY EXCLUSIVE EVENTS

58. Consider the following pairs of events. Drawing a Queen Drawing an Ace Drawing a red suit Drawing a Face Card Q♦ Q♠ Q♥ Q♣ A♦ A♠ A♥ A♣ Drawing a Queen Drawing an Ace Drawing a Diamond Drawing a Red Face Card A♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦ J♥ Q ♥ K♥ MUTUALLY EXCLUSIVE EVENTS NON-MUTUALLY EXCLUSIVE EVENTS Can you get an Ace that is a Queen? Can you get a Diamond that is a Red Face Card?

59. Mutually Exclusive Events Events that cannot happen at the same time. In logic, two propositions are mutually exclusive or disjoint if they cannot both be true. Non- mutually Exclusive Events Events are events that can happen at the same time.

60. There is NO intersection or common outcome. There is an intersection or common outcome.

61. EXAMPLES 1. A: Getting a 7; B: Getting a jack 2. C: Getting a club; D: Getting a king 3. E: Getting a face card; F: Getting an ace 4. G: Getting a face card; H: Getting a spade Determine which events are mutually exclusive and which are not, when a single card is drawn from a deck. Mutually Exclusive Events Non-Mutually Exclusive Events   Mutually Exclusive Events Non-Mutually Exclusive Events  

62. EXAMPLES 1. A: Getting an odd number; B: Getting an even number 2. C: Getting a 3; D: Getting an odd number 3. E: Getting an odd number; F: Getting a number less than 4 4. G: Getting a number less than 4; H: Getting a number greater than 4 Determine which events are mutually exclusive and which are not, when a single die is tossed. Mutually Exclusive Events Non-Mutually Exclusive Events   Non-Mutually Exclusive Events   Mutually Exclusive Events

63. Activity 1: For nos. 1-3, a card is drawn from a standard deck. 1. Event A: A spade is drawn. Event B: A diamond is drawn. 2. Event A: A heart is drawn. Event B: A king is drawn. 3. Event A: An ace is drawn. Event B: A club is drawn. Tell whether the events in each item are mutually exclusive or non-mutually exclusive. Mutually Exclusive Events Non-Mutually Exclusive Events Non-Mutually Exclusive Events

64. Activity 1: 4. One student is selected as the class monitor. Event A: Jay is selected as the monitor. Event B: James is selected as the monitor. For numbers 5-6. A jar contains 2 green balls, 2 red balls, and 1 blue ball. A ball is drawn from it. 5. Event A: You get a red ball. Event B: You get a green ball. 6. Event A: You get a blue ball. Event B: You get a primary colored ball. Tell whether the events in each item are mutually exclusive or non-mutually exclusive. Mutually Exclusive Events Mutually Exclusive Events Non-Mutually Exclusive Events Primary colors are RED, BLUE and YELLOW

65. Probability of the Union of Two Events

66. PROBABILITY OF THE UNION OF TWO EVENTS Union of Mutually Exclusive Events  

67. EXAMPLES 1. A box contains 3 glazed doughnuts, 4 jelly doughnuts, and 5 chocolate doughnuts. If a person selects a doughnut at random, find the probability that it is either a glazed doughnut or a chocolate doughnut. The probability that a glazed doughnut is selected is:   The probability that a chocolate doughnut is selected is:     The probability that either a glazed or a chocolate doughnut is selected is:      

68. EXAMPLES 2. Two dice are rolled. Find the probability of rolling a sum of 8 or 9. The event of rolling a sum of 8 is:       The probability of rolling a sum of 8 or 9 is:       Thus: The event of rolling a sum of 9 is:   Thus:  

69. EXAMPLES 3. Two dice are rolled. Find the probability of rolling a sum of at most 6. The event of rolling a sum of at most 6 means: rolling a sum of 6 or 5 or 4 or 3 or 2     The event for each case are as follows:        

70. EXAMPLES 3. Two dice are rolled. Find the probability of rolling a sum of at most 6.                  

71. PROBABILITY OF THE UNION OF TWO EVENTS Union of Non-Mutually Exclusive Events  

72. EXAMPLES 1. A single card is drawn at random from an ordinary deck of cards. Find the probability that it is either an ace or a black card. The probability of drawing an ace is:   The probability drawing a black card is:     The probability of drawing a black ace is:       Since there are black aces, then the events are non-mutually exclusive . Therefore, the probability of drawing an ace or a black card is:  

73. EXAMPLES 2. In a hospital unit there are 8 nurses and 5 physicians; 7 nurses and 3 physicians are females. If a staff person is selected, find the probability that the subject is a nurse or a male.              

74. EXAMPLES 3. A survey is conducted in an STE class to determine whether they like Analytic Geometry, Biotechnology or Chemistry. A student is selected at random. Let A = event that the student likes Analytic Geometry , B = event that he/she likes Biotechnology , and C = event that he/she likes Chemistry . The probability for each event is taken and illustrated in the Venn Diagram below. What is the probability that the selected student likes: a. Analytic Geometry or Chemistry? b. Biotechnology or Chemistry? c. Analytic Geometry or Biotechnology? d. NEITHER of the three subjects? U                          

75. EXAMPLES 4. Consider the set of all integers from 11 to 150. If an integer is selected from the set, what is the probability that it is divisible by either 4 or 7?   The numbers divisible by 4 in the set are 12, 16, 20, 24, …, 148.      

76. EXAMPLES 4. Consider the set of all integers from 11 to 150. If an integer is selected from the set, what is the probability that it is divisible by either 4 or 7?   The numbers divisible by 4 in the set are 12, 16, 20, 24, …, 148.               Do the same to determine the outcomes that are divisible by 7

77. EXAMPLES 4. Consider the set of all integers from 11 to 150. If an integer is selected from the set, what is the probability that it is divisible by either 4 or 7?   The numbers divisible by 7 in the set are 14, 21, 28, 35, …, 147.              

78. EXAMPLES 4. Consider the set of all integers from 11 to 150. If an integer is selected from the set, what is the probability that it is divisible by either 4 or 7?        

79. EXAMPLES 4. Consider the set of all integers from 11 to 150. If an integer is selected from the set, what is the probability that it is divisible by either 4 or 7?   The numbers divisible by 28 in the set are 28, 56, …, 140.              

80. EXAMPLES 4. Consider the set of all integers from 11 to 150. If an integer is selected from the set, what is the probability that it is divisible by either 4 or 7?          

81. Activity 2: 1. Given the spinner on the right, determine the ff. probabilities: a. P(2 or 5) b. P(6 or odd number) c. P(prime number or factor of 8) d. P(at least 4) 2. In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females, and 12 of the juniors are males. If a student is selected at random, find the probability of selecting the following. [ Hint: Make a frequency table. ] a. A junior or a female b. A senior or a female c. A junior or a senior Solve each problem below accordingly.           Junior Senior Total Male 12 4 16 Female 6 6 12 Total 18 10 28          

82. Activity 2: 3. The diagram on the right shows the distribution of the students who were asked about their preferred subjects. If a student is chosen randomly, find the following: a. the number of students surveyed a. P(Spanish or Chemistry) b. P(Chemistry or Math) c. P(Neither Spanish nor Math) 4. Consider the set of all integers from 1 to 100. If an integer is selected from the set, what is the probability that it is divisible by 5 or by 2? Solve each problem below accordingly.            

83. Activity 2: 3. The diagram on the right shows the distribution of the students who were asked about their preferred subjects. If a student is chosen randomly, find the following: a. the number of students surveyed a. P(Spanish or Chemistry) b. P(Chemistry or Math) c. P(Neither Spanish nor Math) 4. Consider the set of all integers from 1 to 100. If an integer is selected from the set, what is the probability that it is divisible by 5 or by 2? Solve each problem below accordingly.

84. Generalization Differentiate mutually exclusive events from non-mutually exclusive events. How do you find the probability of the union of two events if: A. the events are mutually exclusive? B. the events are non-mutually exclusive?

85. DAY 4 EVALUATION

86. EVALUATION Solve the following problems. What is the probability that a card drawn from a standard deck of 52 cards is a queen or an ace? What is the probability that a die thrown turns up to be odd or even? The probability that a boy will watch PBB is 0.6 and the probability that his sister will watch the same reality show is 0.5. The probability that these children will watch PBB together is 0.3. What is the probability that at least one of the siblings will watch PBB? In a certain country, the probability that it will rain on a day in January is 0.70; the chance that it will snow is 0.35, and the chance that it will rain and snow is 0.17. What is the probability that it will rain or snow for a day for a given month? What is the probability that a card drawn from a standard deck of 52 cards is a face card or a diamond? If one card is drawn at random from a standard deck of cards, what is the probability of randomly selecting an 8 or a black card?

87. EVALUATION 7. What is the probability that a pair of dice turns up to be a pair or has a total of 8? 8. A standard six-sided die is rolled once. What is the probability that it turns up to be a multiple of 3 or even? 9. What is the probability that a card drawn from a standard deck of 52 cards is a number between 3 and 9 or a red card? 10. If a fair six-sided die is rolled, what is the probability of rolling an odd number or a number less than or equal to 3? 11. A restaurant serves a bowl of candies to its customers. The bowl of candies Gabriel received has 10 chocolate candies, 8 coffee candies, and 12 caramel candies. After Gabriel chooses a candy, he eats it. Find the probability of getting candies with the indicated flavors. a. P(chocolate or coffee) c. P(coffee or caramel) b. P(caramel or not coffee) d. P(chocolate or not caramel)

88. EVALUATION 12. Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team? 13. A school’s fair committee consists of 6 girls and 9 boys. One-half of the girls and one-third of the boys are from Grade 10. The committee elected a chairman. What is the probability that the chairman is a girl or a Grade 10? 15. In a class of 60 college students, 20 are girls. One-fourth of the girls and one-fifth of the boys wear glasses. If a student is chosen at random, what is the probability that the student is a girl or wears glasses? 16. The numbers 1, 2,…, 30 are written on slips of paper, put in a box and mixed thoroughly. One number is picked at random. Find the probability that the number is even or a multiple of 5?

89. Checking of Independent Practice

90. INDEPENDENT PRACTICE Solve the following problems. What is the probability that a card drawn from a standard deck of 52 cards is a queen or an ace? What is the probability that a die thrown turns up to be odd or even? The probability that a boy will watch PBB is 0.6 and the probability that his sister will watch the same reality show is 0.5. The probability that these children will watch PBB together is 0.3. What is the probability that at least one of the siblings will watch PBB? In a certain country, the probability that it will rain on a day in January is 0.70; the chance that it will snow is 0.35, and the chance that it will rain and snow is 0.17. What is the probability that it will rain or snow for a day for a given month? 5. What is the probability that a card drawn from a standard deck of 52 cards is a face card or a diamond? 6. If one card is drawn at random from a standard deck of cards, what is the probability of randomly selecting an 8 or a black card?   1        

91. INDEPENDENT PRACTICE 7. What is the probability that a pair of dice turns up to be a pair or has a total of 8? 8. A standard six-sided die is rolled once. What is the probability that it turns up to be a multiple of 3 or even? 9. What is the probability that a card drawn from a standard deck of 52 cards is a number between 3 and 9 or a red card? 10. If a fair six-sided die is rolled, what is the probability of rolling an odd number or a number less than or equal to 3? 11. A restaurant serves a bowl of candies to its customers. The bowl of candies Gabriel received has 10 chocolate candies, 8 coffee candies, and 12 caramel candies. After Gabriel chooses a candy, he eats it. Find the probability of getting candies with the indicated flavors. a. P(chocolate or coffee) c. P(coffee or caramel) b. P(caramel or not coffee) d. P(chocolate or not caramel)                

92. INDEPENDENT PRACTICE 12. Of 240 students, 176 are o n the honor roll, 48 are members of the varsity team, and 36 are on the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team? 13. A school’s fair committee consists of 6 girls and 9 boys. One-half of the girls and one-third of the boys are from Grade 10. The committee elected a chairman. What is the probability that the chairman is a girl or a Grade 10? 15. In a class of 60 college students, 20 are girls. One-fourth of the girls and one-fifth of the boys wear glasses. If a student is chosen at random, what is the probability that the student is a girl or wears glasses? 16. The numbers 1, 2,…, 30 are written on slips of paper, put in a box and mixed thoroughly. One number is picked at random. Find the probability that the number is even or a multiple of 5?        

93. WHLT 6 REVIEWER

94. Differentiate experimental probability from theoretical probability. What is the biggest value of probability? When does this happen? Gian decided to buy different colors of face masks through online shopping. He ordered 10 black, 7 blue, 5 red, and 8 green. When he received the shipment, he was excited to open it. What is the probability that the first mask that he will pick up from the box is black? The letters of the word STATISTICS are placed in a jar. What is the probability of choosing the letter T? What is the probability of getting a number less than 4 in rolling a single die? Fritz flipped a coin 10 times and recorded the outcomes as follow: {H, T, T, T, H, H, H, H, H, T}, where H represents head and T represents the tail. Find P(tail). A committee has 6 female and 10 male members. What is the probability of choosing a female as the chairman of the committee? The numbers 1-20 are written on separate sheets of paper, rolled, and placed in a box. A piece of rolled paper is drawn from the box. What is the probability that the number picked is a prime number?

95. A bag has 1 green, 2 red, 3 purple, 4 white, and 5 black marbles. What is the probability of choosing any colored marble? A die is rolled and a coin is flipped. a. How many possible outcomes are there in the experiment? b. What is the probability that a number 6 or a head will appear? c. What is the probability that an even number or a tail will appear?

97. In a particular school with 200 male students, 58 play football, 40 play basketball, and 8 play both. What is the probability that a randomly selected male student plays football or basketball? If a student is selected at random from those 3 sections, what is the probability that a. he/she takes Cookery or he/she belongs to 10- Rizal? b. ne/she belongs to 10- Mabini or he/she takes Drafting?

98. There are 5 black, 3 blue, 2 yellow, and 1 red ball in a jar. DJ picks a ball without looking. What is the probability that DJ picks a red or a yellow ball? Rhea rolls a six-sided number cube (a die). a. What is the probability that the number rolled is a 4 or a number less than 3? b. What is the probability that the number rolled is an even number or a 1? From a standard deck of cards, what is the probability of picking a heart or a diamond?