Ignition Your friend said that you lost your marbles. However, you found them in a bag and it contained 24 marbles: 6 green, 6 red, and 12 blue. 1. Draw a number line on a sheet of paper and label it with three numbers; one that represents an impossible outcome, one that represents a certain outcome, and one that represents an outcome that is as likely as unlikely. 2. Place the letter on your number line at the location that corresponds to each of the following events: a. Choosing a purple marble b. Choosing a marble c. Choosing a blue marble d. Choosing a green marble e. Choosing a blue or red marble
Independent and Dependent Events Learning Objectives: Students can determine the probability of independent and dependent events. Essential Question: What is the difference between determining the probability of an independent event and a dependent event?
Vocabulary Independent Events the outcome of one event does not affect the outcome of a second event. If A and B are independent events, then P(A, then B) = P(A) P(B) Dependent Events the outcome of one event affects the outcome of a second event. If A and B are dependent events, the P(A, then B) = P(A) (B after A)
Independent Events The below table shows the colors of 20 soccer shirts on a rack. A clerk selects one shirt, puts a price tag on it, replaces it, and then selects again. Find the probability that the first shirt is blue and the second is red. Color P(blue, then red) = P(blue) P(red) Number of Shirts Blue 6 Red 4 Black 3 Orange 7 What is the probability of selecting an orange shirt, replacing it, and then a black shirt?
Independent Events You play a game in which you roll a 6-sided cube. Each of its six faces has a different color. To win, you must select the color rolled. Find the probability of playing the game twice and winning both times.
Dependent Events Two girls and three boys volunteer to speak at a school assembly. Their names are put in a hat. One name is selected at random and not replaced. Then another name is selected. Find P(girl, then girl). Are these independent or dependent events? Why? First Drawing: P(girl) = 2 5 Two of the five volunteers are girls. Second Drawing: P(girl, after girl) = 1 One girl is left of your volunteers. 4 P(girl, then girl) = P(girl) P(girl after girl) = 2 1 5 4 = 2 = 1 20 10 What is the probability that a boy and then a girl are selected? 3 10
Summary You should be able to: -find the probability of independent and dependent events. In Your Planner: Homework: Page 613, problems 1-3, 7-9, 13-14, 20.
State Assessment Prep Sign out an ipad, and go to: sbac.portal.airast.org/practice-test -Click the square with the words Student Interface Practice and Training Tests -Click Sign In -Select Grade: 7 - School Guest: Select Yes - Click Start G7 Math Practice Test - On the next page, select yes and on the next page, select Yes, Start my Test, and then select Begin Test Now
Check for Understanding 1. A video game company sampled 20 shipments of a particular video game. 10 of the games were in incorrect packaging. The company found software problems in 5 of the shipments. For 300 shipments, predict the number of video games that will have software problems. 2. Patton students that received a ROAR card were entered into a raffle for an X-Box 360. The ROAR cards of 40 students were placed in a container. Fifteen 7 th graders, ten 8 th graders and fifteen 9 th graders had tickets in the box. a. What is the probability that a 7 th or 8 th grader will be selected? b. If two tickets are selected, and the first ticket is not returned to the box, what is the probability a 8 th grader, and then a 7 th grader will be selected?
Challenge Problems 1. In a town, 45% of all households have a pet and 35% have children. 40% of all households with children have a pet. A household is chosen at random. Find the probability of that household: a. having no children, but a pet b. having neither children nor a pet c. having children, but not pets. 2. In a middle school with 200 students, 40% are girls. 20% of the students wear glasses. It is also known that 10% of the boys wear glasses. a. How many boys are in this school? b. How many girls don t wear glasses? c. How many students are boys and wear glasses?