Independent and 9 7 Dependent Events PreAlgebra HOMEWORK

Independent and 9 -7 Dependent Events Pre-Algebra HOMEWORK Page 474 #1 -16 Turn in for Credit! Pre-Algebra

Independent and 9 -7 Dependent Events Pre-Algebra HOMEWORK Page 480 #1 -12 Pre-Algebra

Independent and 9 -7 Dependent Events Warm Up Problem of the Day Lesson Presentation Pre-Algebra

Independent and 9 -7 Dependent Events Today’s Learning Goal Assignment Learn to find the probabilities of independent and dependent events. Pre-Algebra

Independent and 9 -7 Dependent Events Vocabulary independent events Pre-Algebra

Independent and 9 -7 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. Pre-Algebra

Independent and 9 -7 Dependent Events Brain. Pop Video login: kyrene; password: brainpop Handout the Quiz AFTER the video! http: //www. brainpop. com/math/pro bability/independentanddependent events/ Pre-Algebra

Independent and 9 -7 Dependent Events Brain. Pop Video Quiz • Handout the video quiz AFTER the video • Each student should complete it independently and silently • Have the students turn in their quiz when they finish it • Continue with the Power. Point lesson Pre-Algebra

Independent and 9 -7 Dependent Events Additional Example 1: Classifying Events as Independent or Dependent Determine if the events are dependent or independent. A. getting tails on a coin toss and rolling a 6 on a number cube Tossing a coin does not affect rolling a number cube, so the two events are independent. B. getting 2 red gumballs out of a gumball machine After getting one red gumball out of a gumball machine, the chances for getting the second red gumball have changed, so the two events are dependent. Pre-Algebra

Independent and 9 -7 Dependent Events Try This: Example 1 Determine if the events are dependent or independent. A. rolling a 6 two times in a row with the same number cube The first roll of the number cube does not affect the second roll, so the events are independent. B. a computer randomly generating two of the same numbers in a row The first randomly generated number does not affect the second randomly generated number, so the two events are independent. Pre-Algebra

Independent and 9 -7 Dependent Events Pre-Algebra

Independent and 9 -7 Dependent Events Additional Example 2 A: 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. A. 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. 1 In each box, P(blue) =. 2 P(blue, blue) = 1 · 1 = 0. 125 Multiply. 2 2 2 8 Pre-Algebra

Independent and 9 -7 Dependent Events Try This: Example 2 A Two boxes each contain 4 marbles: red, blue, green, and black. One marble is chosen from each box. A. 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. 1 In each box, P(blue) =. 4 P(blue, blue) = 1 4 Pre-Algebra · 1 1 = = 0. 0625 4 16 Multiply.

Independent and 9 -7 Dependent Events Additional Example 2 B: Finding the Probability of Independent Events B. What is the probability of choosing a blue marble, then a green marble, and then a blue marble? 1. 2 1 In each box, P(green) =. 2 In each box, P(blue) = P(blue, green, blue) = 1 2 Pre-Algebra · 1 2 · 1 1 = = 0. 125 Multiply. 2 8

Independent and 9 -7 Dependent Events Try This: Example 2 B Two boxes each contain 4 marbles: red, blue, green, and black. One marble is chosen from each box. B. What is the probability of choosing a blue marble and then a red marble? 1 In each box, P(blue) =. 4 1 In each box, P(red) =. 4 P(blue, red) = Pre-Algebra 1 4 · 1 1 = = 0. 0625 4 16 Multiply.

Independent and 9 -7 Dependent Events Additional Example 2 C: Finding the Probability of Independent Events C. What is the probability of choosing at least one blue marble? Think: P(at least one blue) + P(not blue, not blue) = 1. 1 In each box, P(not blue) =. 2 P(not blue, not blue) = 1 1 Multiply. = = 0. 125 · · 2 2 2 8 Subtract from 1 to find the probability of choosing at least one blue marble. 1 – 0. 125 = 0. 875 Pre-Algebra

Independent and 9 -7 Dependent Events Try This: Example 2 C Two boxes each contain 4 marbles: red, blue, green, and black. One marble is chosen from each box. C. What is the probability of choosing at least one blue marble? Think: P(at least one blue) + P(not blue, not blue) = 1. 1 In each box, P(blue) =. 4 P(not blue, not blue) = 3 · 3 = 9 = 0. 5625 Multiply. 4 4 16 Subtract from 1 to find the probability of choosing at least one blue marble. 1 – 0. 5625 = 0. 4375 Pre-Algebra

Independent and 9 -7 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. Pre-Algebra

Independent and 9 -7 Dependent Events Additional Example 3 A: Find the Probability of Dependent Events The letters in the word dependent are placed in a box. A. If two letters are chosen at random, what is the probability that they will both be consonants? P(first consonant) = 6 = 2 9 3 Pre-Algebra

Independent and 9 -7 Dependent Events Additional Example 3 A 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) = 5 8 5 2 · 5 = 12 3 8 Multiply. The probability of choosing two letters that are both consonants is 5. 12 Pre-Algebra

Independent and 9 -7 Dependent Events Try This: Example 3 A The letters in the phrase I Love Math are placed in a box. A. If two letters are chosen at random, what is the probability that they will both be consonants? P(first consonant) = 5 9 Pre-Algebra

Independent and 9 -7 Dependent Events Try This: Example 3 A Continued If the first letter chosen was a consonant, now there would be 4 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) = 5 5 · 1 = 18 9 2 4 = 1 8 2 Multiply. The probability of choosing two letters that are both consonants is 5. 18 Pre-Algebra

Independent and 9 -7 Dependent Events Additional Example 3 B: Find the Probability of Dependent Events B. If two letters are chosen at random, what is the probability that they will both be consonants or both be vowels? There are two possibilities: 2 consonants or 2 vowels. The probability of 2 consonants was calculated in Example 3 A. Now find the probability of getting 2 vowels. Find the probability that P(first vowel) = 3 = 1 the first letter chosen is a 9 3 vowel. If the first letter chosen was a vowel, there are now only 2 vowels and 8 total letters left in the box. Pre-Algebra

Independent and 9 -7 Dependent Events Additional Example 3 B Continued 1 P(second vowel) = 2 = 4 8 Find the probability that the second letter chosen is a vowel. 1 1 · 1 = Multiply. 12 3 4 The events of both consonants and both vowels are mutually exclusive, so you can add their probabilities. 5 1 = 6 = 1 + 2 12 12 12 P(consonant) + P(vowel) The probability of getting two letters that are either both consonants or both vowels is 1. 2 Pre-Algebra

Independent and 9 -7 Dependent Events Try This: Example 3 B B. If two letters are chosen at random, what is the probability that they will both be consonants or both be vowels? There are two possibilities: 2 consonants or 2 vowels. The probability of 2 consonants was calculated in Try This 3 A. Now find the probability of getting 2 vowels. Find the probability that 4 P(first vowel) = the first letter chosen is a 9 vowel. If the first letter chosen was a vowel, there are now only 3 vowels and 8 total letters left in the box. Pre-Algebra

Independent and 9 -7 Dependent Events Try This: Example 3 B Continued P(second vowel) = 3 8 Find the probability that the second letter chosen is a vowel. 12 = 1 4 · 3 = Multiply. 72 9 8 6 The events of both consonants and both vowels are mutually exclusive, so you can add their probabilities. 5 1 = 8 = 4 + 9 18 18 6 P(consonant) + P(vowel) The probability of getting two letters that are either both consonants or both vowels is 4. 9 Pre-Algebra

Independent and 9 -7 Dependent Events Lesson Quiz Determine if each event is dependent or independent. 1. drawing a red ball from a bucket and then drawing a green ball without replacing the first dependent 2. spinning a 7 on a spinner three times in a row independent 3. 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? 5 33 Pre-Algebra