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TOC #6  Independent and Dependent Events

TOC #6  Independent and Dependent Events. MATH 7/8 Set Theory and Probability Unit 1. Vocabulary. 1. Compound event – made up of one or more separate events. 2. Independent events – when one event does not affect the probability of the other.

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TOC #6  Independent and Dependent Events

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  1. TOC #6  Independent and Dependent Events MATH 7/8 Set Theory and Probability Unit 1

  2. Vocabulary 1. Compound event – made up of one or more separate events. 2. Independent events – when one event does not affect the probability of the other. 3. Dependent events – when one event does affect the probability of the other.

  3. Independent OR Dependent?? A. getting tails on a coin toss and rolling a 6 on a number cube B. getting 2 red gumballs out of a gumball machine • rolling a 6 two times in a row with the same number cube • D. a computer randomly generating two of the same numbers in a row

  4. To find the probability of INDEPENDENT events:

  5. 12 In each box, P(blue) = . Example #1 Three separate boxes each have one blue marble and one green marble. One marble is chosen from each box. What is the probability of choosing a blue marble from each box? P(blue, blue, blue) =

  6. Example #2 What is the probability of choosing a blue marble, then a green marble, and then a blue marble?

  7. Example #3 Two boxes each contain 4 marbles: red, blue, green, and black. One marble is chosen from each box. What is the probability of choosing a blue marble from each box? What is the probability of choosing a blue marble and then a red marble?

  8. To find the probability of DEPENDENT events: To calculate the probability of two dependent events occurring, do the following: 1. Calculate the probability of the first event. 2. Calculate the probability that the second event would occur if the first event had already occurred. 3. Multiply the probabilities.

  9. Example #4 The letters in the word dependent are placed in a box. If two letters are chosen at random, what is the probability that they will both be consonants? Because the first letter is not replaced, the sample space is different for the second letter, so the events are dependent.

  10. Example #5 The letters in the word dependent are placed in a box. If two letters are chosen at random, what is the probability that they will both be consonants or both be vowels?

  11. Remember! Two mutually exclusive events cannot both happen at the same time. Mutually Exclusive! The events of both consonants and both vowels are mutually exclusive, so you can add their probabilities.

  12. Example #6 A bucket contains 5 yellow and 7 red balls. If 2 balls are selected randomly without replacement, what is the probability that they will both be yellow?

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