Transcript of "12.8 independent and dependent events"
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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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Lesson 12.8 , For use with pages 694-700 2. You choose an M or P. 1. You choose an O. You choose a card at random from a bag which contains cards with the letters in the word MONOPOLY. Find the ODDS . 1 3 = ANSWER 3 5 ANSWER 2 6
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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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EXAMPLE 3 Finding Probability of Dependent Events Bingo SOLUTION You need B 7 and N 44 for bingo. Find the probability of success when each of the next 2 numbers is drawn. Then multiply. You are playing the bingo card shown. The caller has 50 numbers left to call. What is the probability that you will get bingo with the next 2 numbers called?
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EXAMPLE 3 Finding Probability of Dependent Events P ( B 7 or N 44) There are 50 numbers left to call. Multiply the probabilities. There are 49 numbers left to call. = 1 25 P ( remaining number ) = 1 49 P ( both numbers ) = 1 25 1 49 = 1225 1 ANSWER The probability that you will get bingo when the next 2 numbers are called is, or about 0.0008 . 1225 1 2 50 =
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<ul><li>Use a tree diagram to figure the probability </li></ul><ul><li>The weather forecast for the weekend is for 20% chance of rain on Saturday and a 60% chance of rain on Sunday. Find the probability: </li></ul><ul><ul><li>It will rain both days. </li></ul></ul><ul><ul><li>It will NOT rain either day. </li></ul></ul><ul><ul><li>It will rain only one day of the weekend. </li></ul></ul>
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<ul><li>Use a tree diagram to figure the probability </li></ul><ul><li>The weather forecast for the weekend is for 20% chance of rain on Saturday and a 60% chance of rain on Sunday. </li></ul>Rain No rain Rain No rain Rain No rain Saturday Sunday 0.20 0.80 0.60 0.40 0.60 0.40
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<ul><li>Find the probability: </li></ul><ul><ul><li>It will rain both days. </li></ul></ul><ul><ul><li>It will NOT rain either day. </li></ul></ul><ul><ul><li>It will rain only one day of the weekend. </li></ul></ul>0.20 x 0.60 = 0.12 0.80 x 0.40 = 0.32 0.20 x 0.40 = 0.08 0.80 x 0.60 = 0.48 0.08 + 0.48 = 0.56 Rain No rain Rain No rain Saturday Sunday Rain No rain 0.20 0.80 0.60 0.40 0.60 0.40
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<ul><li>While shooting free throw, Seth has an 80% chance of making his first free throw, but only a 60% chance of making the second free throw. Find the probability: </li></ul><ul><li>--- he will make both free throws. </li></ul><ul><li>--- he will make the first an miss the 2 nd . </li></ul><ul><li>--- he will miss both shots. </li></ul>
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<ul><li>While shooting free throw, Seth has an 80% chance of making his first free throw, but only a 60% chance of making the second free throw. </li></ul>Miss Make Miss Make Miss Make First Second 0.20 0.80 0.40 0.60 0.40 0.60
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<ul><li>Find the probability: </li></ul><ul><ul><li>he will make both free throws. </li></ul></ul><ul><ul><li>he will make the first and miss the 2nd. </li></ul></ul><ul><ul><li>he will miss both shots. </li></ul></ul>0.8 x 0.6 = 0.48 0.8 x 0.4 = 0.32 0.2 x 0.4 = 0.08 Miss Make Miss Make Miss Make First Second 0.20 0.80 0.40 0.60 0.40 0.60
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Animated Math <ul><li>Go to: </li></ul><ul><ul><li>www.classzone.com </li></ul></ul><ul><ul><li>Select your book (lower left hand book) </li></ul></ul><ul><ul><li>Animations </li></ul></ul><ul><ul><li>Chapter 10-13 </li></ul></ul><ul><ul><li>Chapter 12: Independent and Dependent Events </li></ul></ul>
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