Section 4-4
Probability of Compound Events
Essential Questions

How do you find probabilities of compound events?

What are mutua!y exclusive compound events?



Wher...
Vocabulary

1. Compound Event:


2. Mutua!y Exclusive Events:
Vocabulary

1. Compound Event: An event that is made up of two
    or more simpler events

2. Mutua!y Exclusive Events:
Vocabulary

1. Compound Event: An event that is made up of two
    or more simpler events

2. Mutua!y Exclusive Events: Ev...
Example 1
Two 6-sided dice are rolled. Is P(sum is at least 8)
         less than or greater than 50%?
Example 1
Two 6-sided dice are rolled. Is P(sum is at least 8)
         less than or greater than 50%?
  Sample Space:
Example 1
Two 6-sided dice are rolled. Is P(sum is at least 8)
         less than or greater than 50%?
  Sample Space: (6)...
Example 1
Two 6-sided dice are rolled. Is P(sum is at least 8)
         less than or greater than 50%?
  Sample Space: (6)...
Example 1
Two 6-sided dice are rolled. Is P(sum is at least 8)
         less than or greater than 50%?
  Sample Space: (6)...
Example 1
Two 6-sided dice are rolled. Is P(sum is at least 8)
         less than or greater than 50%?
  Sample Space: (6)...
Example 1
Two 6-sided dice are rolled. Is P(sum is at least 8)
         less than or greater than 50%?
  Sample Space: (6)...
Example 2
Two 6-sided dice are rolled.
 Find P(the sum is 5 or 12).
Example 2
Two 6-sided dice are rolled.
 Find P(the sum is 5 or 12).
   36 possible outcomes
Example 2
           Two 6-sided dice are rolled.
            Find P(the sum is 5 or 12).
              36 possible outcom...
Example 2
           Two 6-sided dice are rolled.
            Find P(the sum is 5 or 12).
              36 possible outcom...
Example 2
          Two 6-sided dice are rolled.
           Find P(the sum is 5 or 12).
             36 possible outcomes
...
Example 2
          Two 6-sided dice are rolled.
           Find P(the sum is 5 or 12).
             36 possible outcomes
...
Example 2
          Two 6-sided dice are rolled.
           Find P(the sum is 5 or 12).
              36 possible outcomes...
Example 2
          Two 6-sided dice are rolled.
           Find P(the sum is 5 or 12).
             36 possible outcomes
...
Example 2
          Two 6-sided dice are rolled.
           Find P(the sum is 5 or 12).
             36 possible outcomes
...
Example 2
          Two 6-sided dice are rolled.
           Find P(the sum is 5 or 12).
             36 possible outcomes
...
Example 3
  From nine students (Trevor, Tyler, Davin,
  Chrisla, Tarah, Samantha, Isaac, Tony, and
 Rachel), the teacher w...
Example 3
  From nine students (Trevor, Tyler, Davin,
  Chrisla, Tarah, Samantha, Isaac, Tony, and
 Rachel), the teacher w...
Example 3
 Venn Diagram
Example 3
 Venn Diagram
Example 3
 Venn Diagram
Girl
Example 3
 Venn Diagram
Girl     T-name
Example 3
 Venn Diagram
Girl     T-name


          Trevor
Example 3
 Venn Diagram
Girl     T-name


          Trevor
           Tyler
Example 3
 Venn Diagram
Girl     T-name


          Trevor
                   Davin
           Tyler
Example 3
     Venn Diagram
    Girl     T-name


Chrisla       Trevor
                       Davin
               Tyler
Example 3
     Venn Diagram
    Girl     T-name


Chrisla           Trevor
                           Davin
          Tara...
Example 3
      Venn Diagram
     Girl     T-name


 Chrisla         Trevor
                          Davin
Samantha Tarah...
Example 3
      Venn Diagram
     Girl     T-name


 Chrisla         Trevor
                          Davin
Samantha Tarah...
Example 3
      Venn Diagram
     Girl     T-name


 Chrisla         Trevor
                          Davin
Samantha Tarah...
Example 3
      Venn Diagram
     Girl     T-name


 Chrisla         Trevor
                          Davin
Samantha Tarah...
Example 3

P(Girl or T-name)
Example 3

P(Girl or T-name)
    7
  =
    9
Example 3

P(Girl or T-name)
   7
  = ≈ 77.78%
   9
Homework
Homework

                  p. 164 #1-25



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Integrated Math 2 Section 4-4

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  • Integrated Math 2 Section 4-4

    1. 1. Section 4-4 Probability of Compound Events
    2. 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. 3. Vocabulary 1. Compound Event: 2. Mutua!y Exclusive Events:
    4. 4. Vocabulary 1. Compound Event: An event that is made up of two or more simpler events 2. Mutua!y Exclusive Events:
    5. 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. 6. Example 1 Two 6-sided dice are rolled. Is P(sum is at least 8) less than or greater than 50%?
    7. 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. 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. 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. 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. 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. 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. 13. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12).
    14. 14. Example 2 Two 6-sided dice are rolled. Find P(the sum is 5 or 12). 36 possible outcomes
    15. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 25. Example 3 Venn Diagram
    26. 26. Example 3 Venn Diagram
    27. 27. Example 3 Venn Diagram Girl
    28. 28. Example 3 Venn Diagram Girl T-name
    29. 29. Example 3 Venn Diagram Girl T-name Trevor
    30. 30. Example 3 Venn Diagram Girl T-name Trevor Tyler
    31. 31. Example 3 Venn Diagram Girl T-name Trevor Davin Tyler
    32. 32. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Tyler
    33. 33. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Tarah Tyler
    34. 34. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Samantha Tarah Tyler
    35. 35. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Samantha Tarah Tyler Isaac
    36. 36. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Samantha Tarah Tyler Isaac Tony
    37. 37. Example 3 Venn Diagram Girl T-name Chrisla Trevor Davin Samantha Tarah Tyler Isaac Rachel Tony
    38. 38. Example 3 P(Girl or T-name)
    39. 39. Example 3 P(Girl or T-name) 7 = 9
    40. 40. Example 3 P(Girl or T-name) 7 = ≈ 77.78% 9
    41. 41. Homework
    42. 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

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