Lesson 15.5: Independent and Dependent Events Sep 26 10:07 PM 1
Work with a partner. You have three marbles in a bag. There are two green marbles and one purple marble. Randomly draw a marble from the bag. Then put the marble back in the bag and draw a second marble. a. Complete the tree diagram. Let G = green and P = purple. Find the probability that both marbles are green. GG GG GP GG GP PG PG PP b. Does the probability of getting a green marble on the second draw depend on the color of the first marble? Explain. No! The marble is put back, so they don't impact each other. Activity 1 2
Work with a partner. Using the same marbles from Activity 1, randomly draw two marbles from the bag. a. Complete the tree diagram. Let G = green and P = purple. Find the probability that both marbles are green. GG GP GG PG PG b. Does the probability of getting a green marble on the second draw depend on the color of the first marble? Explain. Yes! If green is first, then there is a 50% chance that green will also be second. If purple is first, there is a 100% chance that green will be second. Activity 2 3
What is the difference between dependent and independent events? Dependent events affect each other. Independent events do not. Essential Question 4
You have a deck of playing cards (4 suits, 13 cards in each suit). Give an example of dependent events and independent events using the deck of cards. Dependent: Picking 2 face cards in a row, without replacement. Independent: Picking a heart, replacing it, and then picking another heart. Closure 5
Tell whether the events are independent or dependent. Explain. 1. You roll a number cube twice. The first roll is a 3 and the second roll is an odd number. Independent the outcome of the first roll does not affect the outcome of the second. 2. You flip a coin twice. The first flip is heads and the second flip is tails. Independent the outcome of the first flip does not affect the outcome of the second. 3. You randomly draw a marble from a bag containing 3 red marbles and 5 blue marbles. You keep the marble and then draw a second marble. Dependent Because the first marble is not replaced, the number of possible outcomes changes with the second draw. 4. You randomly draw a marble from a bag containing 6 red marbles and 2 blue marbles. You put the marble back and then draw a second marble. Independent The marble picked first is replaced. Warm up 6
(Just like 15.4) Key Idea 7
You spin the spinner and flip the coin. What is the probability of spinning a prime number and flipping tails? (2, 3, and 5 are prime) Example 1 8
1. What is the probability of spinning a multiple of 2 and flipping heads? On your own 1 9
Look at as a totally different event Key Idea 10
People are randomly chosen to be game show contestants from an audience of 100 people. You are with 5 of your relatives and 6 other friends. What is the probability that one of your relatives is chosen first, and then one of your friends is chosen second? P (relative first) = P (friend second) = Because one person has already been chosen, there are only 99 people left from which to choose. P (relative first) X P (friend second) = Example 2 11
2. What is the probability that you, your relatives, and your friends are not chosen to be either of the first two contestants? When the first contestant is chosen, there are 88 favorable outcomes (a person outside of your group is chosen), and 100 possible outcomes. After the second contestant is chosen, there is one fewer favorable outcome, as well as one fewer possible outcome. On Your Own 2 12
A student randomly guesses the answer for each of the multiplechoice questions. What is the probability of answering all three questions correctly? There is only one favorable outcome (for each of the 3 questions), because there is only one correct answer. Example 3 13
3. The student can eliminate Choice A for all three questions. What is the probability of answering all three questions correctly? Compare this probability with the probability in Example 3. What do you notice? The probability almost doubles. On your own 3 14
Exit Ticket: You and your friend are among 5 volunteers to help distribute workbooks. What is the probability that your teacher randomly selects you and your friend to distribute the workbooks? Favorable outcomes: either you or your friend are chosen Possible outcomes: 5 volunteers from which to choose Favorable outcomes: you or your friend (whoever wasn't chosen first) Possible outcomes: 4 volunteers left from which to choose Closure 15