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COMP 170 L2 L15: Probability of Unions of Events Objective: The inclusion-exclusion principle for probability Page 1

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Page 1: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

L15: Probability of Unions of Events

Objective:

The inclusion-exclusion principle for probability

Page 1

Page 2: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2Page 2

Page 3: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

Page 4: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

Example: Roll Two DicePage 4

Page 5: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2Page 5

Page 6: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2Page 6

Page 7: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

Page 8: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

NotationPage 8

Page 9: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2Page 9

Page 10: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

Example: BackpackPage 10

Page 11: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

Backpack ProblemPage 11

Page 12: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

Backpack ProblemPage 12

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COMP 170 L2

BackpackPage 13

Page 14: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

BackpackPage 14

Page 15: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

2nd eventPage 15

Page 16: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

2nd eventPage 16

Page 17: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

2nd event

Page 18: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

2nd event

3rd event

Page 18

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COMP 170 L2Page 19

Page 20: COMP 170 L2 L15: Probability of Unions of Events l Objective: n The inclusion-exclusion principle for probability Page 1

COMP 170 L2

Proof of Theorem 5.3

See course notes