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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Write each answer as a ratio, as a decimal, and as a percent. A 1–6 number cube is rolled. 1. What is the probability that an even number will result? 2. What is the probability that the number will be prime?. 1 2.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Write each answer as a ratio, as a decimal, and as a percent. A 1–6 number cube is rolled. 1. What is the probability that an even number will result? 2. What is the probability that the number will be prime? 1 2 , 0.5, 50% 1 2 , 0.5, 50%

  3. California Standards SDAP3.5 Understand the difference between independent and dependent events. Also covered:SDAP3.3, SDAP3.4

  4. Objective: You will learn how to (YWLHT) identify independent and dependent events and find the probability of independent events.

  5. Vocabulary independent events dependent events

  6. Raji and Kara must each choose a topic from a list of topics to research for their class. If Raji can choose the same topic as Kara and vice versa, the events are independent. For independent events, the occurrence of one event has no effect on the probability that a second event will occur. If once Raji chooses a topic, Kara must choose from the remaining topics, then the events are dependent. For dependent events, the occurrence of one event does have an effect on the probability that a second event will occur.

  7. Example 1: Determining Whether Events Are Independent or Dependent Decide whether the set of events are dependent or independent. Explain your answer. A. Kathi draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube. Since the outcome of drawing the card does not affect the outcome of rolling the cube, the events are independent.

  8. Example 2: Determining Whether Events Are Independent or Dependent Decide whether the set of events are dependent or independent. Explain your answer. B. Yuki chooses a book from the shelf to read, and then Janette chooses a book from the books that remain. Since Janette cannot pick the same book that Yuki picked, and since there are fewer books for Janette to choose from after Yuki chooses, the events are dependent.

  9. Example 3: Determining Whether Events Are Independent or Dependent Decide whether the set of events are dependent or independent. Explain your answer. C. Imad chooses a pencil from a drawer, puts it back, and then chooses a second pencil. Both pencils are red. The drawer holds the same pencils each time. Since Imad replaces the first pencil, the outcome of picking the first pencil does not affect the outcome of picking the second pencil. The events are independent.

  10. Check It Out! Example 4 Decide whether the set of events are dependent or independent. Explain your answer. A. Joann flips a coin and gets a head. Then she rolls a 6 on a number cube. Since flipping the coin does not affect the outcome of rolling the number cube, the events are independent.

  11. Check It Out! Example 5 Decide whether the set of events are dependent or independent. Explain your answer. B. Annabelle chooses a blue marble from a set of three, each of different colors, and then Louise chooses a second marble from the remaining two marbles. Since they are picking from the same set of three marbles, they cannot pick the same color marble. The events are dependent.

  12. Check It Out! Example 6 Decide whether the set of events are dependent or independent. Explain your answer. C. Lisa chooses a pen from a bag, puts it back, and then chooses a second pen. Both pens are blue. The bag holds the same pens each time. Since Lisa replaces the first pen, the outcome of picking the first pen does not affect the outcome of picking the second pen. The events are independent.

  13. To find the probability that two independent events will happen, multiply the probabilities of the two events. Probability of Two Independent Events P(A and B) P(B) P(A) • = Probability of first event Probability of both events Probability of second event

  14. Example 7: Finding the Probability of Independent Events Find the probability of choosing a green marble at random from a bag of 5 green and 10 white marbles and then flipping a coin and getting tails.

  15. 1 3 1 2 = · Example 7: Finding the Probability of Independent Events Find the probability of choosing a green marble at random from a bag of 5 green and 10 white marbles and then flipping a coin and getting tails. The outcome of choosing the marble does not affect the outcome of flipping the coin, so the events are independent. P(green and tails) = P(green)· P(tails) The probability of choosing a green marble and a coin landing on tails is . 1 6

  16. Check It Out! Example 8 Find the probability of choosing a red marble at random from a bag containing 5 red and 5 white marbles and then flipping a coin and getting heads.

  17. Check It Out! Example 8 Find the probability of choosing a red marble at random from a bag containing 5 red and 5 white marbles and then flipping a coin and getting heads. The outcome of choosing the marble does not affect the outcome of flipping the coin, so the events are independent. 1 2 1 2 · P(red and heads) = P(red)· P(heads) = The probability of choosing a red marble and a coin landing on heads is . 1 4

  18. Example 9: Sports Application A basketball player has a 60% chance of making a free throw on each attempt. If the chance of making one free throw is independent of the chance of making the next free throw, what is the probability that the player will make 2 free throws in a row? P(making 1st free throw and 2nd free throw) = P(1st free throw) ∙ P(2nd free throw)

  19. Example 9 Continued Substitute 60% for P(1st free throw) and 60% for P(2nd free throw). = 60% ∙ 60% = 0.60 ∙ 0.60 Write the percents as decimals. = 0.36 Multiply. = 36% Write the decimal as a percent. The probability of the basketball player making 2 free throws in a row is 36%.

  20. Check It Out! Example 10 A professional bowler has a 40% chance of bowling a strike on each attempt. If the chance of bowling a strike is independent of the chance of bowling a strike in the next frame, what is the probability that the player will bowl 2 strikes in a row? P(1st strike and 2nd strike) = P(1st strike) ∙ P(2nd strike)

  21. Check It Out! Example 10 Continued Substitute 40% for P(1st strike) and 40% for P(2nd strike). = 40% ∙ 40% = 0.40 ∙ 0.40 Write the percents as decimals. = 0.16 Multiply. = 16% Write the decimal as a percent. The probability of the professional bowler bowling 2 strikes in a row is 16%.

  22. Home Learning On-Line Tutoring Take a Chance! Fishing! Games! Pondability

  23. 3 16 Decide whether each event is independent or dependent. Explain. 1. Mary chooses a game piece from a board game, and then Jason chooses a game piece from three remaining pieces. 2.Find the probability of spinning an evenly divided spinner numbered 1–8 and getting a composite number on one spin and getting an odd number on a second spin. Lesson Quiz Dependent; Jason has fewer pieces from which to choose. 3. A baseball player has a 10% chance of hitting the ball on each turn at bat. What is the probability that the player will hit the ball on each of his next 2 turns at bat? 1%

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