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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
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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
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Essential Questions <ul><li>What are the differences between permutations and combinations? </li></ul><ul><li>What are the differences between odds and probability? </li></ul><ul><li>How is probability used to make predictions? </li></ul><ul><li>What are the differences between experimental and theoretical probabilities? </li></ul>
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<ul><li>Events that contain more than one outcome are called compound events . </li></ul><ul><li>Sometime the occurrence of one event affects the probability of the second event, and sometimes it has no effect. </li></ul><ul><li>If there is no effect , we say the events are independent events . </li></ul><ul><li>Dependent events – events for which the occurrence of one AFFECTS the probability of the other. </li></ul>
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<ul><li>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) </li></ul><ul><li>This is the Multiplication Property for compound events </li></ul>
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Independent or Dependent? <ul><li>A number cube is rolled twice. </li></ul><ul><li>It is raining outside and the parade is canceled. </li></ul><ul><li>The first roll of a number cube is 4, and the sum of the first two rolls is 5. </li></ul><ul><li>It is sunny and a movie theater changes its movie. </li></ul><ul><li>Two cards are drawn, one after the other, from a deck of cards. The first card drawn is not replaced. </li></ul><ul><li>Joey got an A on his math test so he will get an A on his science test. </li></ul>Independent Dependent Dependent Independent Dependent Independent
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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
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<ul><li>5 blue </li></ul><ul><li>6 yellow </li></ul><ul><li>11 red </li></ul><ul><li>8 green </li></ul><ul><li>30 total </li></ul><ul><li>Probability of yellow, yellow with replacement </li></ul><ul><li>Probability of yellow, yellow without replacement </li></ul><ul><li>Probability of red, blue with replacement </li></ul><ul><li>Probability of red, blue without replacement </li></ul><ul><li>Probability of green, yellow with replacement </li></ul><ul><li>Probability of green, yellow without replacement </li></ul>
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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 =
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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
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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
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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
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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
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