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Example 5-3b Objective Find the probability of independent and dependent events

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Example 5-3b Vocabulary Compound Event An event that consists of two or more simple events

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Example 5-3b Vocabulary Independent Events Two or more events in which the outcome of one event does not affect the outcome of the other event(s)

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Example 5-3b Vocabulary Dependent events Two or more events in which the outcome of one event does affect the outcome of the other event(s)

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Lesson 5 Contents Example 1Probability of Independent Events Example 2Use Probability to Solve a Problem Example 3Probability of Dependent Events

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Example 5-1a The two spinners below are spun. What is the probability that both spinners will show a number greater than 6? 1/3 Write probability statement for the 1 st spinner P(greater than 6) = Write the formula for probability Numbers greater than 6 Total Numbers

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Example 5-1a The two spinners below are spun. What is the probability that both spinners will show a number greater than 6? 1/3 P(greater than 6) = Count the numbers greater than 6 for the numerator Numbers greater than 6 Total Numbers P(greater than 6) = 3

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Example 5-1a The two spinners below are spun. What is the probability that both spinners will show a number greater than 6? 1/3 P(greater than 6) = Count the total numbers for the denominator Numbers greater than 6 Total Numbers P(greater than 6) = 3 10

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Example 5-1a The two spinners below are spun. What is the probability that both spinners will show a number greater than 6? 1/3 The second spinner is exactly like the 1 st spinner except for color so same probability P(greater than 6) = 3 10 P(greater than 6) = 3 10

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Example 5-1a The two spinners below are spun. What is the probability that both spinners will show a number greater than 6? 1/3 Write the probability statement for both spinners P(greater than 6) = 3 10 P(greater than 6) = 3 10 P(both spinners greater than 6) = Multiply the probability of each spinner 3 10 3 Use calculator to multiply P(both spinners greater than 6) = 9 100 Answer: NOTE: Independent event since neither spinner affected the other

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Example 5-1b The two spinners below are spun. What is the probability that both spinners will show a number less than 4? Answer: P (both spinners less than 4) = 1/3

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Example 5-2a What is the probability that a student picked at random will be an eighth-grade girl? Girls Boys Cross River Middle School Grade 8 Grade 7 Grade 6 Fraction of the Population Demographic Group 2/3 Write probability statement for an eighth-grade girl P(8 th grade girl) =

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Example 5-2a What is the probability that a student picked at random will be an eighth-grade girl? Girls Boys Cross River Middle School Grade 8 Grade 7 Grade 6 Fraction of the Population Demographic Group 2/3 Note: Data is given in fractions which can be used as a probability! P(8 th grade girl) =

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Example 5-2a What is the probability that a student picked at random will be an eighth-grade girl? Girls Boys Cross River Middle School Grade 8 Grade 7 Grade 6 Fraction of the Population Demographic Group 2/3 Write probability of 8 th grade P(8 th grade girl) = Put multiplication sign Write probability of girl

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Example 5-2a What is the probability that a student picked at random will be an eighth-grade girl? Girls Boys Cross River Middle School Grade 8 Grade 7 Grade 6 Fraction of the Population Demographic Group 2/3 Multiply P(8 th grade girl) = Answer: NOTE: Independent event since neither probability affected the other probability

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Example 5-2b POPULATION Use the information below. What is the probability that a student picked at random will be a sixth grade boy? Answer: Girls Boys Monterey Middle School Grade 8 Grade 7 Grade 6 Fraction of the Population Demographic Group Probability (6 th grade boy) = 2/3

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Example 5-3a There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen. 3/3 Since the sock is not put back, it will affect the probability of the second sock chosen This is a dependent event Write probability statement for the first sock chosen P(1 st sock blue) =

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Example 5-3a There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen. 3/3 Numerator is number of blue socks This is a dependent event P(1 st sock blue) = 6 Denominator is total number of socks in drawer 18

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Example 5-3a There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen. 3/3 This is a dependent event P(1 st sock blue) = 6 18 Write probability statement for the second sock chosen P(2 nd sock blue) = Numerator is number of blue socks minus the one not replaced 5 Denominator is total number of socks in drawer minus the one not replaced 17

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Example 5-3a There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen. 3/3 This is a dependent event P(1 st sock blue) = 6 18 Write probability statement for both socks P(2 nd sock blue) = 5 17 P(both socks blue) = Multiply the two probabilities of the 2 socks chosen Multiply P(both socks blue) = Answer:

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Example 5-3b There are 6 green, 9 purple, and 3 orange marbles in a bag. Once a marble is selected, it is not replaced. Find the probability that two purple marbles are chosen. Answer: P (two purple marbles) = * 3/3

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End of Lesson 5 Assignment Lesson 8:5 Probability of Compound Events 4 - 26 All

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