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Understanding Probability of Independent and Dependent Events

Learn how to calculate the probabilities of independent and dependent events with examples using spinners, number cubes, and bags of cards and socks. Practice finding the likelihood of events occurring together in compound events.

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Understanding Probability of Independent and Dependent Events

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  1. Lesson Menu Main Idea and New Vocabulary Key Concept: Probability of Independent Events Example 1: Independent Events Example 2: Independent Events Key Concept: Probability of Dependent Events Example 3: Real-World Example

  2. Find the probability of independent and dependent events. • compound event • independent events • dependent events Main Idea/Vocabulary

  3. Key Concept

  4. Independent Events The two spinners below are spun. What is the probability that both spinners will show a number greater than 6? Example 1

  5. P(spinning number > 6 on spinner 1) = P(spinning number > 6 on spinner 2) = P(both numbers are > 6) = = Answer: The probability that both spinners will show a number greater than 6 is Independent Events Example 1

  6. A. B. C. D. Two number cubes are rolled. The faces of the number cubes are labeled 1–6. What is the probability rolling a 1 or a 2 on both number cubes? Example 1 CYP

  7. Independent Events A red number cube and a white number cube are rolled. The faces of both cubes are numbered from 1 to 6. What is the probability of rolling a 3 on the red number cube and rolling a 3 or less on the white number cube? You are asked to find the probability of rolling a 3 on the red number cube and rolling a 3 or less on the white number cube. The events are independent because rolling the red number cube does not affect the outcome of rolling the white number cube. Example 2

  8. P(3 on red cube) = P(3 or less on white cube) = Independent Events First, find the probability of each event. Example 2

  9. P(3 on red cube and 3 or less on white cube) = P(A and B) = P(A) P(B) = Multiply. Answer: The probability is Independent Events Then find the probability of both events occurring. Example 2

  10. A. B. C. D. A bag contains cards with the letters A–F written on them, each letter represented once. A second bag has cards with the colors yellow, green, and blue written on them, each color represented once. What is the probability of drawing a vowel from the first bag and the color yellow from the second bag? Example 2 CYP

  11. Key Concept 3

  12. SOCKS There are 4 red, 8 yellow, and 6 blue socks mixed up in a drawer. Once a sock is selected, it is not replaced. Find the probability of reaching into the drawer without looking and choosing 2 blue socks. Example 3

  13. number of blue socks total number of socks number of blue socks after one blue sock is removed total number of socks after one sock is removed Answer: The probability is Since the first sock is not replaced, the first event affects the second event. These are dependent events. Example 3

  14. A. B. C. D. CANDY There are 3 butterscotch candies, 7 peppermints, and 4 cinnamon candies in a candy bowl. Donna selects a piece of candy at random and then Jake selects a piece of candy at random. Find the probability that both choose a butterscotch candy. Example 3 CYP

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