Warm Up Multiply. Write each fraction in simplest form. 1. 2.  Write each fraction as a decimal

Independent and Dependent Events 10-4 Learn to find the probabilities of independent and dependent events.

Independent and Dependent Events 10-4 A compound event is made up of two 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.

Independent and Dependent Events 10-4 Determine if the events are dependent or independent. 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 Example 1: Classifying Events as Independent or Dependent Tossing a coin does not affect rolling a number cube, so the two events are independent. 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.

Independent and Dependent Events 10-4 Determine if the events are dependent or independent. A. rolling a 6 two times in a row with the same number cube B. a computer randomly generating two of the same numbers in a row Example 2 The first roll of the number cube does not affect the second roll, so the events are independent. The first randomly generated number does not affect the second randomly generated number, so the two events are independent.

Independent and Dependent Events 10-4 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? Example 3: Finding the Probability of Independent Events The outcome of each choice does not affect the outcome of the other choices, so the choices are independent. P(blue, blue, blue) = In each box, P(blue) = · 1212 · 1212 = 1818 = Multiply.

Independent and Dependent Events 10-4 What is the probability of choosing a blue marble, then a green marble, and then a blue marble? Example 4: Finding the Probability of Independent Events P(blue, green, blue) = 1212 · 1212 · 1212 = 1818 = Multiply. In each box, P(blue) = In each box, P(green) =. 1212

Independent and Dependent Events 10-4 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? Example 5 The outcome of each choice does not affect the outcome of the other choices, so the choices are independent. In each box, P(blue) = P(blue, blue) = 1414 · 1414 = 1 16 = Multiply.

Independent and Dependent Events 10-4 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? Example 6 In each box, P(blue) = P(blue, red) = 1414 · 1414 = 1 16 = Multiply. In each box, P(red) =. 1414

Independent and Dependent Events 10-4 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.

Independent and Dependent Events 10-4 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? Example 7: Find the Probability of Dependent Events P(first consonant) = = 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.

Independent and Dependent Events 10-4 Continue Example 7 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) = ·= The probability of choosing two letters that are both consonants is Multiply.

Independent and Dependent Events 10-4 There are 6 red gumballs, 4 yellow, 8 green, and 2 blue. Once one is picked, it is NOT replaced. What is the probability you will draw a blue first, then red, then yellow?

Independent and Dependent Events 10-4 Two mutually exclusive events cannot both happen at the same time. Remember!

Independent and Dependent Events 10-4 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

Independent and Dependent Events 10-4 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 2. spinning a 7 on a spinner three times in a row 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? independent dependent 5 33

Independent and Dependent Events Identify the dependent event. A. drawing an apple from a basket and then drawing an orange without replacing the apple B. drawing an apple from a basket and then drawing an orange after replacing the apple C. getting a 3 and then a 2 when a fair number cube is rolled twice D. spinning an even number on a spinner two times in a row Lesson Quiz for Student Response Systems

Independent and Dependent Events Identify the independent event. A. pulling out a white sock and then a blue sock from a dresser B. choosing a student from 7th Grade and a student from 8th Grade C. drawing a six and then a diamond from a deck of well shuffled cards D. choosing three members from a club Lesson Quiz for Student Response Systems

Independent and Dependent Events The letters in the word PROBABILITY are placed in a box. If two cards are chosen at random, what is the probability that they will both have the letter B? A. B. C. D. Lesson Quiz for Student Response Systems