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Section 5.3 - The Addition Rule and Disjoint Events

Section 5.3 - The Addition Rule and Disjoint Events. D16. The diagrams at the bottom of the slide are called Venn diagrams. How do these diagrams justify the two forms of the Addition Rule?. Section 5.3 - The Addition Rule and Disjoint Events.

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Section 5.3 - The Addition Rule and Disjoint Events

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  1. Section 5.3 - The Addition Rule and Disjoint Events D16. The diagrams at the bottom of the slide are called Venn diagrams. How do these diagrams justify the two forms of the Addition Rule?

  2. Section 5.3 - The Addition Rule and Disjoint Events D16. How do these Venn diagrams justify the two forms of the Addition Rule? Non-disjoint events Disjoint events

  3. Section 5.3 - The Addition Rule and Disjoint Events D17. What happens to the general form of the Addition Rule in a situation where A and B are mutually exclusive? Mutually exclusive

  4. Section 5.3 - The Addition Rule and Disjoint Events D17. What happens to the general form of the Addition Rule in a situation where A and B are mutually exclusive? Mutually exclusive

  5. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. In categorizing people who fish, are these three categories disjoint? Are they complete? Suppose you randomly select a person from among those who fish. Can you find the probability that the person fishes in salt water? Can you find the probability that the person fishes in fresh water? The number of people who fish in fresh water is 28,439,000. How many people fish in both salt water and fresh water?

  6. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. In categorizing people who fish, are these three categories disjoint? Are they complete?

  7. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. In categorizing people who fish, are these three categories disjoint? Are they complete? The three categories are not disjoint: 1847000 + 27913000 + 9051000 > 34071000 The categories are completesince people who fish must belong to at least one of these three categories.

  8. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. Suppose you randomly select a person from among those who fish. Can you find the probability that the person fishes in salt water?

  9. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. Suppose you randomly select a person from among those who fish. Can you find the probability that the person fishes in salt water? Yes:

  10. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. Can you find the probability that the person fishes in fresh water?

  11. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. Can you find the probability that the person fishes in fresh water? You can’t find the probability that the person fishes in fresh water, since the “Great Lakes” and “other fresh water” categories overlap.

  12. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. The number of people who fish in fresh water is 28,439,000. How many people fish in both salt water and fresh water?

  13. Section 5.3 - The Addition Rule and Disjoint Events P14. Of the 34,071,000 people in the U.S. who fish, 1,847,000 fish in the Great Lakes, 27,913,000 fish in other fresh water, and 9,051,000 fish in salt water. The number of people who fish in fresh water is 28,439,000. How many people fish in both salt water and fresh water? The number of people who fish in fresh water is 28,439,000. The number of people who fish in both salt water and fresh water is fresh or salt = fresh + salt - (fresh and salt) fresh and salt = fresh + salt - (fresh or salt) fresh and salt = 28,439,000 + 9,051,000 - 34,071,000 = 3,419,000

  14. Section 5.3 - The Addition Rule and Disjoint Events P15. Display 5.33 categorizes the child support received by custodial parents with children under age 21. Revise the table so that the categories are complete and disjoint. One category was not included: With agreement or award but not supposed to receive payment in 2001

  15. Section 5.3 - The Addition Rule and Disjoint Events P15. Display 5.33 categorizes the child support received by custodial parents with children under age 21. Revise the table so that the categories are complete and disjoint. One category was not included: With agreement or award but not supposed to receive payment in 2001

  16. Section 5.3 - The Addition Rule and Disjoint Events P15. Display 5.33 categorizes the child support received by custodial parents with children under age 21. Revise the table so that the categories are complete and disjoint. One category was not included: With agreement or award but not supposed to receive payment in 2001

  17. Section 5.3 - The Addition Rule and Disjoint Events P15. Display 5.33 categorizes the child support received by custodial parents with children under age 21. Revise the table so that the categories are complete and disjoint. One category was not included: With agreement or award but not supposed to receive payment in 2001

  18. Section 5.3 - The Addition Rule and Disjoint Events P16. If you roll two dice, are these pairs of events mutually exclusive? Doubles; sum is 8 Doubles; sum is odd A 3 on one die; sum is 10 A 3 on one die; doubles

  19. Section 5.3 - The Addition Rule and Disjoint Events P16. If you roll two dice, are these pairs of events mutually exclusive? Doubles; sum is 8 Doubles; sum is odd A 3 on one die; sum is 10 A 3 on one die; doubles

  20. Section 5.3 - The Addition Rule and Disjoint Events P16. If you roll two dice, are these pairs of events mutually exclusive? Doubles; sum is 8: Not mutually exclusive: Doubles = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)} Sum is 8 = {(2,6),(6,2),(3,5),(5,3),(4,4)}

  21. Section 5.3 - The Addition Rule and Disjoint Events P16. If you roll two dice, are these pairs of events mutually exclusive? Doubles; sum is odd: Mutually exclusive: Doubles = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)} Sum is odd = {(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(3,6),(4,1), (4,3),(4,5),(5,2),(5,4),(5,6),(6,1),(6,3),(6,5)}

  22. Section 5.3 - The Addition Rule and Disjoint Events P16. If you roll two dice, are these pairs of events mutually exclusive? A 3 on one die; sum is 10: Mutually exclusive: A 3 on one die = {(1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6)} Sum is 10 = {(4,6),(5,5),(6,4)}

  23. Section 5.3 - The Addition Rule and Disjoint Events P16. If you roll two dice, are these pairs of events mutually exclusive? A 3 on one die; doubles: Not mutually exclusive: A 3 on one die = {(1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6)} Doubles = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}

  24. Section 5.3 - The Addition Rule and Disjoint Events P17. A researcher will select a student at random from a school population where 33% of the students are freshmen, 27% are sophomores, 25% are juniors, and 15% are seniors. Is it appropriate to use the Addition Rule for Disjoint Events to find the probability that the student will be a junior or a senior? Why or why not? Find the probability that the student will be a freshman or a sophomore.

  25. Section 5.3 - The Addition Rule and Disjoint Events P17. A researcher will select a student at random from a school population where 33% of the students are freshmen, 27% are sophomores, 25% are juniors, and 15% are seniors. Is it appropriate to use the Addition Rule for Disjoint Events to find the probability that the student will be a junior or a senior? Why or why not?

  26. Section 5.3 - The Addition Rule and Disjoint Events P17. A researcher will select a student at random from a school population where 33% of the students are freshmen, 27% are sophomores, 25% are juniors, and 15% are seniors. Is it appropriate to use the Addition Rule for Disjoint Events to find the probability that the student will be a junior or a senior? Why or why not? Yes. A student can’t be a junior and a senior at the same time.

  27. Section 5.3 - The Addition Rule and Disjoint Events P17. A researcher will select a student at random from a school population where 33% of the students are freshmen, 27% are sophomores, 25% are juniors, and 15% are seniors. Find the probability that the student will be a freshman or a sophomore.

  28. Section 5.3 - The Addition Rule and Disjoint Events P17. A researcher will select a student at random from a school population where 33% of the students are freshmen, 27% are sophomores, 25% are juniors, and 15% are seniors. Find the probability that the student will be a freshman or a sophomore.

  29. Section 5.3 - The Addition Rule and Disjoint Events P18. A tetrahedral die has the numbers 1, 2, 3, and 4 on its four faces. Suppose you roll a pair of tetrahedral dice. Make a table of all 16 possible outcomes. Use the Addition Rule for Disjoint Events to find the probability that you get a sum of 6 or a sum of 7. Use the Addition Rule for Disjoint Events to find the probability that you get doubles or a sum of 7. Why can’t you use the Addition Rule for Disjoint Events to find the probability that you get doubles or a sum of 6?

  30. Section 5.3 - The Addition Rule and Disjoint Events P18. A tetrahedral die has the numbers 1, 2, 3, and 4 on its four faces. Suppose you roll a pair of tetrahedral dice. Make a table of all 16 possible outcomes.

  31. Section 5.3 - The Addition Rule and Disjoint Events P18. A tetrahedral die has the numbers 1, 2, 3, and 4 on its four faces. Suppose you roll a pair of tetrahedral dice. Use the Addition Rule for Disjoint Events to find the probability that you get a sum of 6 or a sum of 7.

  32. Section 5.3 - The Addition Rule and Disjoint Events P18. A tetrahedral die has the numbers 1, 2, 3, and 4 on its four faces. Suppose you roll a pair of tetrahedral dice. Use the Addition Rule for Disjoint Events to find the probability that you get a sum of 6 or a sum of 7.

  33. Section 5.3 - The Addition Rule and Disjoint Events P18. A tetrahedral die has the numbers 1, 2, 3, and 4 on its four faces. Suppose you roll a pair of tetrahedral dice. Use the Addition Rule for Disjoint Events to find the probability that you get doubles or a sum of 7.

  34. Section 5.3 - The Addition Rule and Disjoint Events P18. A tetrahedral die has the numbers 1, 2, 3, and 4 on its four faces. Suppose you roll a pair of tetrahedral dice. Use the Addition Rule for Disjoint Events to find the probability that you get doubles or a sum of 7.

  35. Section 5.3 - The Addition Rule and Disjoint Events P18. A tetrahedral die has the numbers 1, 2, 3, and 4 on its four faces. Suppose you roll a pair of tetrahedral dice. Why can’t you use the Addition Rule for Disjoint Events to find the probability that you get doubles or a sum of 6?

  36. Section 5.3 - The Addition Rule and Disjoint Events P18. A tetrahedral die has the numbers 1, 2, 3, and 4 on its four faces. Suppose you roll a pair of tetrahedral dice. Why can’t you use the Addition Rule for Disjoint Events to find the probability that you get doubles or a sum of 6?

  37. Section 5.3 - The Addition Rule and Disjoint Events P19. Display 5.34 gives information about all reportable crashes on state-maintained roads in North Carolina in a recent year.

  38. Section 5.3 - The Addition Rule and Disjoint Events P19. Display 5.34 gives information about all reportable crashes on state-maintained roads in North Carolina in a recent year. Are the events crash involved a teen driver and crash was speed relatedmutually exclusive? How can you tell?

  39. Section 5.3 - The Addition Rule and Disjoint Events P19. Display 5.34 gives information about all reportable crashes on state-maintained roads in North Carolina in a recent year. Are the events crash involved a teen driver and crash was speed relatedmutually exclusive? How can you tell? Not mutually exclusive. Look at the yellow cell.

  40. Section 5.3 - The Addition Rule and Disjoint Events Use numbers from the cells of the table to compute the probability that a randomly selected crash involved a teen driver or was speed related.

  41. Section 5.3 - The Addition Rule and Disjoint Events Use numbers from the cells of the table to compute the probability that a randomly selected crash involved a teen driver or was speed related.

  42. Section 5.3 - The Addition Rule and Disjoint Events Now use two of the marginal totals and one number from a cell of the table to compute the probability that a randomly selected crash involved a teen driver or was speed related.

  43. Section 5.3 - The Addition Rule and Disjoint Events Now use two of the marginal totals and one number from a cell of the table to compute the probability that a randomly selected crash involved a teen driver or was speed related.

  44. Section 5.3 - The Addition Rule and Disjoint Events P20. Use the Addition Rule to compute the probability that if you roll two six-sided dice, You get doubles or a sum of 4 You get doubles or a sum of 7 You get s 5 on the first die or you get a 5 on the second die

  45. Section 5.3 - The Addition Rule and Disjoint Events

  46. Section 5.3 - The Addition Rule and Disjoint Events

  47. Section 5.3 - The Addition Rule and Disjoint Events

  48. Section 5.3 - The Addition Rule and Disjoint Events P21. Use the Addition Rule to compute the probability that if you flip two fair coins, you get heads on the first coin or you get heads on the second coin.

  49. Section 5.3 - The Addition Rule and Disjoint Events P21. Use the Addition Rule to compute the probability that if you flip two fair coins, you get heads on the first coin or you get heads on the second coin.

  50. Section 5.3 - The Addition Rule and Disjoint Events P22. Use the Addition Rule to find the probability that if you roll a pair of dice, you do not get doubles or you get a sum of 8.

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