A in the first experiment randomly draw one marble

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a. In the first experiment, randomly draw one marble from the bag. Put it back. Draw a second marble. Repeat this 36 times. Record each result. Make a bar graph of your results. b. In the second experiment, randomly draw two marbles from the bag 36 times. Record each result. Make a bar graph of your results. Frequency First Experiment Results 15 20 25 0 5 10 30 35 40 GG GP PP Result Frequency Second Experiment Results 15 20 25 0 5 10 30 35 40 GG GP PP Result c. For each experiment, estimate the probability of drawing two green marbles. d. Which experiment do you think represents dependent events ? Which represents independent events ? Explain your reasoning. ACTIVITY: Conducting an Experiment 3 4. IN YOUR OWN WORDS What is the difference between dependent and independent events? Describe a real-life example of each. In Questions 5-7, tell whether the events are independent or dependent . Explain your reasoning. 5. You roll a 5 on a number cube and spin blue on a spinner. 6. Your teacher chooses one student to lead a group, and then chooses another student to lead another group. 7. You spin red on one spinner and green on another spinner. 8. In Activities 1 and 2, what is the probability of drawing a green marble on the first draw? on the second draw? How do you think you can use these two probabilities to find the probability of drawing two green marbles? Use what you learned about independent and dependent events to complete Exercises 3 and 4 on page 433. Use Definitions In what other mathematical context have you seen the terms independent and dependent ? How does knowing these definitions help you answer the questions in part (d)? Math Practice
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430 Chapter 10 Probability and Statistics Lesson 10.5 Lesson Tutorials Compound events may be independent events or dependent events . Events are independent events if the occurrence of one event does not affect the likelihood that the other event(s) will occur. Key Vocabulary independent events, p. 430 dependent events, p. 431 Probability of Independent Events Words The probability of two or more independent events is the product of the probabilities of the events. Symbols P ( A and B ) = P ( A ) P ( B ) P ( A and B and C ) = P ( A ) P ( B ) P ( C ) EXAMPLE Finding the Probability of Independent Events 1 You spin the spinner and flip the coin. What is the probability of spinning a prime number and flipping tails? The outcome of spinning the spinner does not affect the outcome of flipping the coin. So, the events are independent. P (prime) = 3 5 P (tails) = 1 2 Use the formula for the probability of independent events. P ( A and B ) = P ( A ) P ( B ) P (prime and tails) = P (prime) P (tails) = 3 5 1 2 Substitute. = 3 10 Multiply. The probability of spinning a prime number and flipping tails is 3 10 , or 30%. 1. What is the probability of spinning a multiple of 2 and flipping heads?
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