Union and intersection of events (math 10)
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Compound Events: THe Union and intersection of events
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Union and intersection of events (math 10)
- 1. PROBABILITY OF COMPOUND EVENTS Prepared by: LORETO A. ELARDO JR. Math 10 Teacher
- 2. 1. A die is rolled once. Find the probability of obtaining a 1? N=_____ n=_____ P(E)=______
- 3. 2. A die is rolled once. Find the probability of obtaining a number less than 6? N=_____ n=_____ P(E)=______
- 4. 3. A die is rolled once. Find the probability of obtaining a number greater than 4? N=_____ n=_____ P(E)=______
- 5. 4.A box contains 5 red balls, 7 yellow balls, and 6 blue balls. If a ball is pick at random from the box, what is the probability that a ball picked is a Yellow ball? N=_____ n=_____ P(E)=____
- 6. 5.A box contains 5 red balls, 7 yellow balls, and 6 blue balls. If a ball is pick at random from the box, what is the probability that a ball picked is a Red ball? N=_____ n=_____ P(E)=____
- 7. 6.A box contains 5 red balls, 7 yellow balls, and 6 blue balls. If a ball is pick at random from the box, what is the probability that a ball picked is a Blue ball? N=_____ n=_____ P(E)=____
- 8. UNION AND INTERSECTION OF EVENTS OBJECTIVES:
- 9. P R O B A B I L I T Y The theory of probability was founded in the 17th century by two French mathematicians Blaise Pascal and Pierre Fermat.It began with problems related to the games of chance.
- 10. PROBABILITY OF COMPOUND EVENTS Let n = number of outcomes in the event N =number of outcomes in the sample space 𝑷 𝑬 = 𝒏 𝑵
- 18. PROBLEM 1: A die is rolled once. Find the probability of obtaining a 5? N=6; n=1 𝑷 𝑬 = 𝒏 𝑵 𝑷 𝒐𝒃𝒕𝒂𝒊𝒏𝒊𝒏𝒈 𝒂 𝟓 = 𝟏 𝟔 Take note: N=1,2,3,4,5,6
- 19. PROBLEM 1: A die is rolled once. Find the probability of obtaining a 6? N=6; n=1 𝑷 𝑬 = 𝒏 𝑵 𝑷 𝒐𝒃𝒕𝒂𝒊𝒏𝒊𝒏𝒈 𝒂 𝟔 = 𝟏 𝟔
- 20. PROBLEM 2: A box contains 3 red balls, 5 yellow balls, and 2 blue balls. If a ball is pick at random from the box, what is the probability that a ball picked is a Yellow ball? N=3+5+2=10 n=5 𝑷 𝑬 = 𝟓 𝟏𝟎 = 𝟏 𝟐 𝑷 𝒑𝒊𝒄𝒌𝒊𝒏𝒈 𝒚𝒆𝒍𝒍𝒐𝒘 𝒃𝒂𝒍𝒍 = 𝟏 𝟐
- 21. PROBLEM 2: A box contains 3 red balls, 5 yellow balls, and 2 blue balls. If a ball is pick at random from the box, what is the probability that a ball picked is a Red Ball? N=3+5+2=10 n=3 𝑷 𝑬 = 𝟑 𝟏𝟎 𝑷 𝒑𝒊𝒄𝒌𝒊𝒏𝒈 𝒓𝒆𝒅 𝒃𝒂𝒍𝒍 = 𝟑 𝟏𝟎
- 22. PROBLEM 2: A box contains 3 red balls, 5 yellow balls, and 2 blue balls. If a ball is pick at random from the box, what is the probability that a ball picked is a Blue Ball? N=3+5+2=10 n=2 𝑷 𝑬 = 𝟐 𝟏𝟎 = 𝟏 𝟓 𝑷 𝒑𝒊𝒄𝒌𝒊𝒏𝒈 𝒃𝒍𝒖𝒆 𝒃𝒂𝒍𝒍 = 𝟏 𝟓
- 23. PROBLEM 1: A die is rolled once. Find the probability of obtaining an odd number? N=6; n=3 𝑷 𝑬 = 𝒏 𝑵 𝑷 𝒐𝒃𝒕𝒂𝒊𝒏𝒊𝒏𝒈 𝒂𝒏 𝒐𝒅𝒅 𝒏𝒖𝒎𝒃𝒆𝒓 = 𝟑 𝟔 = 𝟏 𝟐 Take note: n=1, 3, 5
- 24. PROBLEM 1: A die is rolled once. Find the probability of obtaining an even number? N=6; n=3 𝑷 𝑬 = 𝒏 𝑵 Take note: n=2, 4, 6 𝑷 𝒐𝒃𝒕𝒂𝒊𝒏𝒊𝒏𝒈 𝒂𝒏 𝒆𝒗𝒆𝒏 𝒏𝒖𝒎𝒃𝒆𝒓 = 𝟑 𝟔 = 𝟏 𝟐
- 25. N=1,2,3,5,6 n=0 𝑷 𝑬 = 𝒏 𝑵
- 27. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Give the sample space of combination of rice, viand , and drink. How many possible outcome are there?
- 28. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice List the possible outcomes of selecting any lunch with pineapple juice.
- 29. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice How many outcomes are there for selecting any lunch with pineapple juice.
- 30. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice How many outcomes are there for selecting a lunch with steamed rice and with pineapple juice?
- 31. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice How many outcomes are there for selecting a lunch with chicken adobo and with pineapple juice?
- 32. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice How many outcomes are there for selecting a lunch with pinakbet and orangejuice?
- 33. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice What is the probability that the student chose pineapple juice as a drink?
- 34. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice What is the probability that the student chose steamed rice and pineapple juice as a drink?
- 35. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice What is the probability that the student chose chicken adobo and orange juice?
- 36. RICE VIAND DRINK Fried rice Steamed rice Chicken adobo Pinakbet Chicken adobo Pinakbet Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice Pineapple juice Orange Juice What is the probability that the student chose pinakbet and pineapple juice?
- 37. 1,1 , 1,2 , 1,3 , 1,4 , 1,5 , (1,6) 2,1 , 2,2 , 2,3 , 2,4 , 2,5 , (2,6) 3,1 , 3,2 , 3,3 , 3,4 , 3,5 , (3,6) 4,1 , 4,2 , 4,3 , 4,4 , 4,5 , (4,6) 5,1 , 5,2 , 5,3 , 5,4 , 5,5 , (5,6) 6,1 , 6,2 , 6,3 , 6,4 , 6,5 , (6,6) 𝑺 = 𝟑𝟔
- 38. 1,1 , 1,2 , 1,3 , 1,4 , 1,5 , (1,6) 2,1 , 2,2 , 2,3 , 2,4 , 2,5 , (2,6) 3,1 , 3,2 , 3,3 , 3,4 , 3,5 , (3,6) 4,1 , 4,2 , 4,3 , 4,4 , 4,5 , (4,6) 5,1 , 5,2 , 5,3 , 5,4 , 5,5 , (5,6) 6,1 , 6,2 , 6,3 , 6,4 , 6,5 , (6,6) 𝐄 = 𝟑, 𝟔 , 𝟒, 𝟓 , 𝟓, 𝟒 , (𝟔, 𝟑)
- 39. 1,1 , 1,2 , 1,3 , 1,4 , 1,5 , (1,6) 2,1 , 2,2 , 2,3 , 2,4 , 2,5 , (2,6) 3,1 , 3,2 , 3,3 , 3,4 , 3,5 , (3,6) 4,1 , 4,2 , 4,3 , 4,4 , 4,5 , (4,6) 5,1 , 5,2 , 5,3 , 5,4 , 5,5 , (5,6) 6,1 , 6,2 , 6,3 , 6,4 , 6,5 , (6,6) E = 3,6 , 4,5 , 5,4 , (6,3)𝐄 = 𝟑, 𝟔 , 𝟒, 𝟓 , 𝟓, 𝟒 , (𝟔, 𝟑)
- 40. PROBABILITY OF COMPOUND EVENTS Compound events are events which consists of more than one outcome.
- 41. Problem 1A: A standard playing card has 52 cards: 4 suits (heart, club, diamond, spade). Each suit has 9 numbers (2 to 10) and ace, king, queen, jack If a card is drawn, find the probability of getting a diamond. N=52; n=13 𝑷 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝒂 𝒅𝒊𝒂𝒎𝒐𝒏𝒅 = 𝟏𝟑 𝟓𝟐 = 𝟏 𝟒
- 42. Problem 1B: A standard playing card has 52 cards: 4 suits (heart, club, diamond, spade). Each suit has 9 numbers (2 to 10) and ace, king, queen, jack If a card is drawn, find the probability of getting an ace. N=52; n=4 𝑷 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝒂𝒏 𝒂𝒄𝒆 = 𝟒 𝟓𝟐 = 𝟏 𝟏𝟑
- 43. Problem 1C: If a card is drawn, find the probability of getting a face card. N=52; n=12𝑷 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝒂 𝒇𝒂𝒄𝒆 𝒄𝒂𝒓𝒅 = 𝟏𝟐 𝟓𝟐 = 𝟑 𝟏𝟑
- 44. Problem 2A: N=C(52,2)= 1326 n=C(26,2)=325 𝑷 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝒐𝒇 𝒕𝒘𝒐 𝒃𝒍𝒂𝒄𝒌 𝒄𝒂𝒓𝒅𝒔 = 𝟑𝟐𝟓 𝟏𝟑𝟐𝟔 = 𝟐𝟓 𝟏𝟎𝟐 If 2 cards are drawn from a standard deck of cards, what is the probability of getting 2 black cards?
- 45. Problem 2B: N=C(52,2)= 1326 n=C(26,1)·C(13,1)= 𝑷 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝒐𝒏𝒆 𝒓𝒆𝒅 𝒄𝒂𝒓𝒅 𝒂𝒏𝒅 𝒐𝒏𝒆 𝒔𝒑𝒂𝒅𝒆 = 𝟑𝟑𝟖 𝟏𝟑𝟐𝟔 = 𝟏𝟑 𝟓𝟏 Two cards are drawn from a standard deck of cards. What is the probability of getting one red card and one is spade? (26)(13)=338
- 46. Problem 3A: N=C(12,3)= 220 n=C(4,3)=4 𝑷 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝟑 𝒑𝒊𝒏𝒌 𝒃𝒂𝒍𝒍𝒔 = 𝟒 𝟐𝟐𝟎 = 𝟏 𝟓𝟓 There are 5 red, 4 pink and 3 blue balls in an urn. If you draw three balls at random, what is the probability that all 3 are pink?
- 47. Problem 3B: N=C(12,3)= 220 n=C(5,2)·C(3,1)=10(3)=30 𝑷 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝟐 𝒓𝒆𝒅 𝒂𝒏𝒅 𝟏 𝒃𝒍𝒖𝒆 = 𝟑𝟎 𝟐𝟐𝟎 = 𝟑 𝟐𝟐 There are 5 red, 4 pink and 3 blue balls in an urn. If you draw three balls at random, what is the probability that 2 are red and one is blue?
- 48. Problem 3C: N=C(12,3)= 220 n=C(3,2)·C(9,1) 𝑷 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝟐 𝒃𝒍𝒖𝒆 = 𝟐𝟕 𝟐𝟐𝟎 There are 5 red, 4 pink and 3 blue balls in an urn. If you draw three balls at random, what is the probability that 2 are blue? =3(9)=27
- 49. Problem 4A: N=48 n=20 𝑷 𝒄𝒉𝒐𝒐𝒔𝒊𝒏𝒈 𝒂 𝒃𝒐𝒚 = 𝟐𝟎 𝟒𝟖 = 𝟓 𝟏𝟐 There are 48 students in Grade 10- Charity. Twenty are boys and 28 are girls. If a teacher randomly selects a student to represent the class in a school meeting, what is the probability that a boy is chosen?
- 50. Problem 4B: N=48 n=28 𝑷 𝒄𝒉𝒐𝒐𝒔𝒊𝒏𝒈 𝒂 𝒈𝒊𝒓𝒍 = 𝟐𝟖 𝟒𝟖 = 𝟕 𝟏𝟐 There are 48 students in Grade 10- Charity. Twenty are boys and 28 are girls. If a teacher randomly selects a student to represent the class in a school meeting, what is the probability that a girl is chosen?
- 51. Problem 4C: N=C(48,3) n=C(28,3) 𝑷 𝒄𝒉𝒐𝒐𝒔𝒊𝒏𝒈 𝟑 𝒈𝒊𝒓𝒍𝒔 = 𝑪 𝟐𝟖, 𝟑 𝑪 𝟒𝟖, 𝟑 There are 48 students in Grade 10- Charity. Twenty are boys and 28 are girls. If a committee of 3 students is formed, what is the probability that all are girls?
- 52. Problem 4D: N=C(48,3) n=C(20,2)·C(28,1) 𝑷 𝒄𝒉𝒐𝒐𝒔𝒊𝒏𝒈 𝟐 𝒃𝒐𝒚𝒔 𝒂𝒏𝒅 𝟏 𝒈𝒊𝒓𝒍 = 𝑪 𝟐𝟎, 𝟐 · 𝑪(𝟐𝟖, 𝟏) 𝑪 𝟒𝟖, 𝟑 There are 48 students in Grade 10- Charity. Twenty are boys and 28 are girls. If a committee of 3 students is formed, what is the probability that two are boys and one is girl?
- 53. Problem 4E: N=C(48,3) n=C(28,1)· 𝑷 𝒄𝒉𝒐𝒐𝒔𝒊𝒏𝒈 𝒂 𝒈𝒊𝒓𝒍 𝒔𝒆𝒄𝒓𝒆𝒕𝒂𝒓𝒚 = 𝑪 𝟐𝟖, 𝟏 · 𝑪(𝟒𝟖, 𝟐) 𝑪 𝟒𝟖, 𝟑 C(48,2) Suppose that a team of 3 students is formed such that it is composed of a team leader, a secretary, and a spokesperson. What is the probability that a team formed is composed of a girl secretary?