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Learn to find the probabilities of independent and dependent events.

Independent and Dependent Events. 10-5. Course 3. Learn to find the probabilities of independent and dependent events. Independent and Dependent Events. 10-5. Course 3. Insert Lesson Title Here. Vocabulary. compound events independent events

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Learn to find the probabilities of independent and dependent events.

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  1. Independent and Dependent Events 10-5 Course 3 Learn to find the probabilities of independent and dependent events.

  2. Independent and Dependent Events 10-5 Course 3 Insert Lesson Title Here Vocabulary compound events independent events dependent events

  3. Independent and Dependent Events 10-5 Course 3 A compound event is made up of one or more separate events. To find the probability of a compound event, you need to know if the events are independent or dependent. Events are independent events if the occurrence of one event does not affect the probability of the other. Events are dependent events if the occurrence of one does affect the probability of the other.

  4. Independent and Dependent Events 10-5 18 12 12 12 12 In each box, P(blue) = . · · = = Course 3 Additional Example 2A: Finding the Probability of Independent Events 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? The outcome of each choice does not affect the outcome of the other choices, so the choices are independent. Multiply. P(blue, blue, blue) = 0.125

  5. Independent and Dependent Events 10-5 In each box, P(green) = . 1 2 12 12 18 12 12 In each box, P(blue) = . · · = = Course 3 Additional Example 2B: Finding the Probability of Independent Events What is the probability of choosing a blue marble, then a green marble, and then a blue marble? Multiply. P(blue, green, blue) = 0.125

  6. Independent and Dependent Events 10-5 In each box, P(not blue) = . 18 12 12 12 1 2 · · = = Course 3 Additional Example 2C: Finding the Probability of Independent Events What is the probability of choosing at least one blue marble? Think: P(at least one blue) + P(not blue, not blue, not blue) = 1. P(not blue, not blue, not blue) = 0.125 Multiply. Subtract from 1 to find the probability of choosing at least one blue marble. 1 – 0.125 = 0.875

  7. Independent and Dependent Events 10-5 14 14 14 14 In each box, P(blue) = . In each box, P(red) = . 1 16 · = = Course 3 Check It Out: Example 2B 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 and then a red marble? Multiply. P(blue, red) = 0.0625

  8. Independent and Dependent Events 10-5 14 34 34 In each box, P(blue) = . 9 16 · = = Course 3 Check It Out: Example 2C Two boxes each contain 4 marbles: red, blue, green, and black. One marble is chosen from each box. What is the probability of choosing at least one blue marble? Think: P(at least one blue) + P(not blue, not blue) = 1. P(not blue, not blue) = 0.5625 Multiply. Subtract from 1 to find the probability of choosing at least one blue marble. 1 – 0.5625 = 0.4375

  9. Independent and Dependent Events 10-5 Course 3 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.

  10. Independent and Dependent Events 10-5 23 69 = Course 3 Additional Example 3A: Find the Probability of Dependent Events 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. Find the probability that the first letter chosen is a consonant. P(first consonant) =

  11. Independent and Dependent Events 10-5 58 58 23 5 12 · = The probability of choosing two letters that are both consonants is . 5 12 Course 3 Additional Example 3A Continued If the first letter chosen was a consonant, now there would be 5 consonants and a total of 8 letters left in the box. Find the probability that the second letter chosen is a consonant. P(second consonant) = Multiply.

  12. Independent and Dependent Events 10-5 13 12 12 14 28 14 = 5 12 6 12 1 12 1 12 · = = = + The probability of getting two letters that are either both consonants or both vowels is . Course 3 Additional Example 3B Continued Find the probability that the second letter chosen is a vowel. P(second vowel) = Multiply. The events of both consonants and both vowels are mutually exclusive, so you can add their probabilities. P(consonant) + P(vowel)

  13. Independent and Dependent Events 10-5 = 49 49 38 38 49 16 5 18 12 72 8 18 1 6 · = = = + The probability of getting two letters that are either both consonants or both vowels is . Course 3 Check It Out: Example 3B Continued Find the probability that the second letter chosen is a vowel. P(second vowel) = Multiply. The events of both consonants and both vowels are mutually exclusive, so you can add their probabilities. P(consonant) + P(vowel)

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