Transcript Slide 1
9.7 Dependent and Independent Events Mr. Swaner Notes Independent events are not influenced by any other event. That is, the event does not depend on what happens elsewhere. Ex. If I am picking out a shirt from my closet and a tie out of my drawer, the number of shirts and number of ties have no effect on the probability of one another. No matter what shirt I pull out of the closet, there are the same number of ties in the drawer. The shirt selection has no effect on the tie selection. Notes Dependent Events are influenced by other events.The probability of the event depends on what happens elsewhere Ex. Let’s say I am taking shirts out of my closet again. The probability of the shirt I pick second will depend on which shirt was pulled out first I have 2 red shirts, a blue shirt, and a green shirt. If my first selection is a green shirt and I don’t put it back, what is the probability that I pick a green shirt the second time? It is impossible! There are none left. Let’s See if We Can Determine if the Probability of Events are Independent or Dependent 1. Getting heads on a coin toss and rolling a 6 on a dice. 2. Getting 3 red gumballs out of a machine of different colors 3. Pulling out two matching socks one at a time from a drawer of mixed socks. 4. A football team wins 2 games in a row. 5. Drawing the names of 2 brothers out of a hat of 10 names Lets Try Some Independent Events 1. Getting heads on a coin toss and rolling a 6 on a dice. What is the probability of getting heads on a coin toss? What is the probability of rolling a 6 on a dice? 1 2 1 6 When determining the overall probability we generally multiply the two probabilities together when the word and is used 1 1 1 2 6 12 When determining the overall probability we generally add the two probabilities when the word or is used More Independent Events 4. A football team wins 2 games in a row. What is the probability of the team winning the first game? 1 2 What is the probability of the team winning the second game? 1 2 The question is really asking,” what is the probability that the team wins the first game and the second game?” are we going to add or multiply? 1 1 1 2 2 4 or 25% Not Today Let’s go back to the first one Getting heads on a coin toss and or rolling a 6 on a dice 1 1 4 2 2 6 6 3 Dependent Events You have a bag of 10 marbles: 3 red, 4 blue, 2 green, and 1 purple. What is the probability of picking red first then green if you only pick two and do not replace them? Probability of picking red = 3 10 Probability of picking green = 2 9 What is the probability of picking red first then green if you only pick two and do not replace them? 3 2 10 9 Another 2. Getting 3 red gumballs in a row out of a machine of different colors There is not enough information here to determine the probability but we know that the probability depends on how many red gumballs there are, and how many gumballs there are total. Let’s say there are 9 red gumballs and 18 gumballs altogether. favorable total 9 18 How many red are left now? that is the odds of getting the first red gumball 8 17 How many total are left now Now we have to get one more red. What is the probability this time? 7 16 Continued 9 18 The odds of getting the first red are: The odds of getting the second red are: The odds of getting the third red are: 7 16 8 17 What are the odds of getting a red and a red and a red in a row? 9 8 7 18 17 16 504 4896 10% Dependent Event Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get 2 black pens? P(black first) = 6 3 or 14 7 5 P(black second) = (There are 13 pens left and 5 are black) 13 THEREFORE……………………………………………… P(black, black) = 3 5 15 or 7 13 91 Dependent Event Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get: P(blue first) = P(black second) = P(blue, black) = Dependent Event Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get: P(blue first) = P(blue second) = P(blue, blue) = TEST YOURSELF Are these dependent or independent events? 1. Tossing two dice and getting a 6 on both of them. 2. You have a bag of marbles: 3 blue, 5 white, and 12 red. You choose one marble out of the bag, look at it then put it back. Then you choose another marble. 3. You have a basket of socks. You need to find the probability of pulling out a black sock and its matching black sock without putting the first sock back. 4. You pick the letter Q from a bag containing all the letters of the alphabet. You do not put the Q back in the bag before you pick another tile. Probability of Dependent Events A basket contains 6 apples, 5 bananas, 4 oranges, and 5 peaches. Leslie randomly chooses one piece of fruit, eats it, then chooses another. What is the probability that she chose a banana and then an apple? Dependent Events Find the probability P(Q, Q) All the letters of the alphabet are in the bag 1 time Do not replace the letter 1 26 0 x 25 0 = 650 0 Probability of Three Dependent Events You and two friends go to a restaurant and order a sandwich. The menu has 10 types of sandwiches and each of you is equally likely to order any type. What is the probability that each of you orders a different type? There are 20 dogs at the dog park. 3 are brown, 9 are black, 6 are white, and 2 are yellow. You will not replace each dog before the next selection. P(white, black) There are 20 dogs at the dog park. 3 are brown, 9 are black, 6 are white, and 2 are yellow. You will not replace each dog before the next selection. P(yellow, yellow) Closure When you see the word AND, that means…….? When you see the word OR, that means……?