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  • 1. By Jaclyn Kogut Independent and Dependent Events 11-3
  • 2. Objectives 
    • Determine whether events are independent or dependent.
    • Find the probability of independent and dependent events.
  • 3. Vocabulary
    • Independent events:
    • Dependent events:
    • The occurrence of one
    • event that does not
    • affect the probability of
    • the other
    • The occurrence of one
    • event that affects the
    • probability of the other
    • Conditional Probability
  • 4. Conditional Probability
    • When finding the probability of dependent events, you use conditional probability.
    • P(B  A) = the probability of event B , given that event A has already occurred
  • 5. Probability of Independent Events
    • If A and B are independent events, then
    • P(A and B) = P(A)  P(B)
  • 6. Example 1: Finding the Probability of Independent Events
    • There is a ten-sided cube: three sides are colored green, two sides are colored red, and five sides are colored blue
    • Find the probability of rolling a green, then red, then blue
  • 7. Example 1: Finding the Probability of Independent Events
    • P(green, then red, and then blue) = P(green)  P(red)  P(blue)
  • 8. Example 1: Finding the Probability of Independent Events Step 1: Find the probability of rolling one green side P(green) = 3/10 Step 2: Find the probability of rolling one red side P(red) = 2/10 = 1/5 Step 3: Find the probability of rolling one blue side P(blue) = 5/10 = 1/2
  • 9. Example 1: Finding the Probability of Independent Events
    • Step 4: Multiply each separate probability by each other
    • P(green, then red, and then blue) = P(green)  P(red)  P(blue)
    • = 3/10  1/5  1/2
    • = 3/100
    • = 0.03 probability
  • 10. Probability of Dependent Events
    • If A and B are dependent events, then
    • P(A and B) = P(A)  P(B  A), where
    • P(B  A) is the probability of B, given that A has already occurred
  • 11. Example 2: Finding the Probability of Dependent Events
    • Two number cubes are rolled - one blue and one white. Explain why the events are dependent and find the probability.
    • The blue cube must show a 5 and the sum of the two cubes must be greater than 8
  • 12. Example 2: Finding the Probability of Dependent Events
    • P(blue 5 and sum  8) = P(blue 5)  P(sum  8  blue 5)
  • 13. Example 2: Finding the Probability of Dependent Events
    • Step 1: Find the probability of blue rolling a 3
    • P(blue 5) = 2/12 = 1/6
    • Step 2: Find the probability of the white cube rolling a number that will make the sum greater than 8
    • P(sum  8  blue 5) = 4/6 = 2/3
  • 14. Example 2: Finding the Probability of Dependent Events
    • Step 3: Multiply each probability together to get the final probability
    • P(blue 5 and sum  8) = P(blue 5)  P(sum  8  blue 5)
    • = 1/6  2/3
    • = 2/18 = 1/9
    • = .11111111111 probability
  • 15. Determine if the event is independent or dependent:
    • Selecting a spade when the first card is taken out of the deck
    • Drawing a queen, putting it back, and then drawing a king
    • Eating all the red skittles and taking out a green skittle
    • Taking out all the green skittles, putting 5 back, eating a purple, and finding a orange skittle
  • 16. THE END