12.8 independent and dependent events   1
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  • 1. 1. You choose an O. 2. You choose an M. You choose a card at random from a bag which contains cards with the letters in the word MONOPOLY. Find the probability. Lesson 12.8 , For use with pages 694-700
  • 2. 1. You choose an O. 2. You choose an M. You choose a card at random from a bag which contains cards with the letters in the word MONOPOLY. Find the probability. Lesson 12.8 , For use with pages 694-700 ANSWER 3 8 ANSWER 1 8
  • 3. Dependent & Independent Events Section 12. 8
  • 4. Essential Questions
    • What are the differences between permutations and combinations?
    • What are the differences between odds and probability?
    • How is probability used to make predictions?
    • What are the differences between experimental and theoretical probabilities?
  • 5.
    • Events that contain more than one outcome are called compound events .
    • Sometime the occurrence of one event affects the probability of the second event, and sometimes it has no effect.
    • If there is no effect , we say the events are independent events .
    • Dependent events – events for which the occurrence of one AFFECTS the probability of the other.
  • 6.
    • If events A and B are independent events, then the probability of A and B occurring is given by P(A & B) = P(A) x P(B)
    • This is the Multiplication Property for compound events
  • 7. Independent or Dependent?
    • A number cube is rolled twice.
    • It is raining outside and the parade is canceled.
    • The first roll of a number cube is 4, and the sum of the first two rolls is 5.
    • It is sunny and a movie theater changes its movie.
    • Two cards are drawn, one after the other, from a deck of cards. The first card drawn is not replaced.
    • Joey got an A on his math test so he will get an A on his science test.
    Independent Dependent Dependent Independent Dependent Independent
  • 8. GUIDED PRACTICE for Examples 1and 2 In Exercises 1 and 2 , tell whether the events are independent or dependent. Explain your reasoning. 1. You toss a coin. Then you roll a number cube. You randomly choose 1 of 10 marbles. Then you randomly choose one of the remaining 9 marbles. 2. The coins toss does not affect the roll of a dice, so the events are independent. ANSWER There is one fewer number in the bag for the second draw, so the events are dependent. ANSWER
  • 9.
    • 5 blue
    • 6 yellow
    • 11 red
    • 8 green
    • 30 total
    • Probability of yellow, yellow with replacement
    • Probability of yellow, yellow without replacement
    • Probability of red, blue with replacement
    • Probability of red, blue without replacement
    • Probability of green, yellow with replacement
    • Probability of green, yellow without replacement
  • 10. EXAMPLE 2 Standardized Test Practice The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss resulting in a win. So the probability of each event is . 1 25 ANSWER The probability of two winning tosses in a row is . 625 1 The correct answer is A . P ( win and win ) = P ( win ) P ( win ) 25 1 1 25 =
  • 11. GUIDED PRACTICE for Examples 1and 2 3. You toss a coin twice. Find the probability of getting two heads. P ( head and head ) = P ( head ) P ( head ) = 1 4 or 25% 1 2 1 2 = The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss ANSWER
  • 12. Daily Homework Quiz For use after Lesson 12. 8 5/10 x 4/9 2. A bag contains ten cards numbered 1 through 10 . You pick one card and then another without replacement. What is the probability that both cards display a value of 6 or higher? ANSWER 2 9 – , 0.2
  • 13. Daily Homework Quiz For use after Lesson 12. 8 1. Events A and B are independent. P(A & B) = P(A) x P(B) P (A) 0.75 , P (B) 0.5 , P (A and B) _____ ANSWER 0.75 x 0.5 = 0.375
  • 14. Daily Homework Quiz For use after Lesson 12. 8 1. Events A and B are dependent. P(A & B) = P(A) x P(B) P (A) 0.75 , P (B given A) _?_ , P (A and B) 0.3 ANSWER 0.3 ÷ 0.75 = 0.4
  • 15. Homework
    • Page 697 #1-9, 17-20, 23-26