HELP ME PLEASE
School: A. Discussion and Examples Probability is the chance that an event will occur. The union of two events is a set that contains all of the elements that are in at least one of the two events. The word that you will often see that indicates a union is "or". The intersection of the two events is a set that contains alll of the elements that are in both events. The word that you will often see that indicates an intersection is "and". Probability of a union of two events Example 1 A fair six-sided die is rolled once, The possible outcomes are {1,2,3,4,5,6}. Let A be the event that the number is an odd number > A={1,3,5) B be the event that the number is greater than 3 1230 B= 14,5,6) C be the event that number is an even number w C={2,4,6} Find the indicated probability: 1. P ( A UB) 2. P (B UC) since (A U B) = {1,3,4,5,6} since (B U C) = [2,4,5,6} therefore P (A U B) = > therefore P (B U C) = = or - 3. P( AUC) 4. P (AnB) since (A U C) = {1,2,3,4,5,6} since (An B) = (5} therefore P (A U C) = 2 or 1 therefore P (An B) = _ 5. P( An C) since (A n C) = { } empty set since there is no common element therefore P (A n C) =0 > the probability of an empty set is zeroExample 2 Thirty students in a room love watching thriller series but 10 among them enjoy drama series also. There are 50 students in the room and 8 of them do not enjoy watching thriller and drama series. Find the probability who enjoys a. thriller b. drama c. thriller or drama d. thriller and drama e. not drama Solution: This situation can be presented through a Venn diagram. 8 a. P (thriller) = 30 50 Or b. P (drama) = 22 11 Thriller Drama 50 or 25 10 c. P (thriller or drama) =P (thriller U drama) 20 12 = = 21 50 25 d. P (thriller and drama) P (thriller n drama ) = 4 or e. P (not drama) = - or 14 25 B. Exercises Exercise 1 Directions: Read carefully the situation and answer the following: Fifteen balls in a jar are numbered from 1 to 15. A ball is drawn at random. Let A be the event that the number on the ball is less than 6 B be the event that the number on the ball is greater than 9 and C be the event that the number on the ball is even. Find the indicated probability: 1. P( AUB) 2. P (B UC) 3. P ( A UC) 4. P (Bn C) 5. P( An B) Exercise 2 Directions: Illustrate the Venn diagram of the given situation and answer the following questions: In a sports event with 35 guests,8 enjoy biking and hiking and 15 enjoy only biking and the rest enjoy hiking only. Determine the probability of the guests who prefer 1. hiking. 2. biking. 3. hiking and biking. 4. hiking or biking. 5. not bikingC. Assessment/ Application/Outputs A. Directions: Choose the letter of the correct answer. Write it in your answer sheet. A number is drawn at random from the set {1,2,3,... 20).Find the probability that the number chosen is 1. A multiple of 2 and a multiple of 5 WIN - 20 B. 1 2. A multiple of 2 or a multiple of 5 D. A- 20 3. A multiple of 3 but not a multiple of 5 A. 1 B. D.- 4. A multiple of 3 or a multiple of 2 A. B. 20 C. D. 70 5. A multiple of 3 and a multiple of 2 A . S 20 C. 20 D. B. Refer to the situation to answer numbers 1-5. A classroom has 25 students, 12 are into sports, 10 are into theater and 4 are into both sports and theater. What is the probability of students who are into 1. sports? 2. theater? 3. sports or theater? 4. sports and theater? 5. not into sports or theater? D. Suggested Enrichment/Reinforcement Activity/ies illustrate the Venn diagram of the given situation and give the indicated probability. There are 52 students in a class and 10 of them like English and Mathematics and 3 of them do not like both subjects,25 students like English only. If a student is selected at random, find the probability that 1. heishe liked Mathematics only. 2. he/she liked English. 3. he/she liked Mathematics. 4. he/she liked both Mathematics and English. 5. he/she liked English or Mathematics
