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Integrated Math 2 Section 4-4

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Probability of Compound Events

Probability of Compound Events

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  • 1. Section 4-4 Probability of Compound Events
  • 2. Essential Questions How do you find probabilities of compound events? What are mutua!y exclusive compound events? Where you’! see this: Games, probability, number sense
  • 3. Vocabulary 1. Compound Event: 2. Mutua!y Exclusive Events:
  • 4. Vocabulary 1. Compound Event: An event that is made up of two or more simpler events 2. Mutua!y Exclusive Events:
  • 5. Vocabulary 1. Compound Event: An event that is made up of two or more simpler events 2. Mutua!y Exclusive Events: Events that cannot occur at the same time
  • 6. Example 1 Two 6-sided dice are rolled. Is P(sum is at least 8) less than or greater than 50%?
  • 7. Example 1 Two 6-sided dice are rolled. Is P(sum is at least 8) less than or greater than 50%? Sample Space:
  • 8. Example 1 Two 6-sided dice are rolled. Is P(sum is at least 8) less than or greater than 50%? Sample Space: (6)(6)
  • 9. Example 1 Two 6-sided dice are rolled. Is P(sum is at least 8) less than or greater than 50%? Sample Space: (6)(6) = 36 possible outcomes
  • 10. Example 1 Two 6-sided dice are rolled. Is P(sum is at least 8) less than or greater than 50%? Sample Space: (6)(6) = 36 possible outcomes (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)
  • 11. Example 1 Two 6-sided dice are rolled. Is P(sum is at least 8) less than or greater than 50%? Sample Space: (6)(6) = 36 possible outcomes (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) P(sum ≥ 8) =
  • 12. Example 1 Two 6-sided dice are rolled. Is P(sum is at least 8) less than or greater than 50%? Sample Space: (6)(6) = 36 possible outcomes (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) 15 P(sum ≥ 8) = 36
  • 13. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12).
  • 14. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes
  • 15. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes Times were sum is 5:
  • 16. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes Times were sum is 5: Times were sum is 12:
  • 17. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes Times were sum is 5: 4 Times were sum is 12:
  • 18. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes Times were sum is 5: 4 Times were sum is 12: 1
  • 19. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes Times were sum is 5: 4 Times were sum is 12: 1 P(sum of 5 or 12)
  • 20. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes Times were sum is 5: 4 Times were sum is 12: 1 4 1 P(sum of 5 or 12) = + 36 36
  • 21. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes Times were sum is 5: 4 Times were sum is 12: 1 4 1 5 P(sum of 5 or 12) = + = 36 36 36
  • 22. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes Times were sum is 5: 4 Times were sum is 12: 1 4 1 5 P(sum of 5 or 12) = + = ≈ 13.89% 36 36 36
  • 23. Example 3 From nine students (Trevor, Tyler, Davin, Chrisla, Tarah, Samantha, Isaac, Tony, and Rachel), the teacher will choose a student at random to work a problem at the chalkboard. What is the probability that the students is a girl or has a name that begins with T?
  • 24. Example 3 From nine students (Trevor, Tyler, Davin, Chrisla, Tarah, Samantha, Isaac, Tony, and Rachel), the teacher will choose a student at random to work a problem at the chalkboard. What is the probability that the students is a girl or has a name that begins with T? P(Girl or T-name)
  • 25. Example 3 Venn Diagram
  • 26. Example 3 Venn Diagram
  • 27. Example 3 Venn Diagram Girl
  • 28. Example 3 Venn Diagram Girl T-name
  • 29. Example 3 Venn Diagram Girl T-name Trevor
  • 30. Example 3 Venn Diagram Girl T-name Trevor Tyler
  • 31. Example 3 Venn Diagram Girl T-name Trevor Davin Tyler
  • 32. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Tyler
  • 33. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Tarah Tyler
  • 34. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Samantha Tarah Tyler
  • 35. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Samantha Tarah Tyler Isaac
  • 36. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Samantha Tarah Tyler Isaac Tony
  • 37. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Samantha Tarah Tyler Isaac Rachel Tony
  • 38. Example 3 P(Girl or T-name)
  • 39. Example 3 P(Girl or T-name) 7 = 9
  • 40. Example 3 P(Girl or T-name) 7 = ≈ 77.78% 9
  • 41. Homework
  • 42. Homework p. 164 #1-25 “Imagination is more important that knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” - Albert Einstein