1. 8th Grade Math Data and Probability Unit Dependent and Independent Events

2. What is a dependent event? If the outcome of one event affects the outcome of another, then the events are said to be Dependent Events. Example: Taking out a marble from a bag containing some marbles and not replacing it, and then taking out a second marble are dependent events.

3. What is an independent event? Independent events are events where the outcome of one event does not affect the outcome of the other events Example: Tossing a coin and rolling a number cube are independent events.

4. New Vocabulary Terms Event – An Event is a one or more outcome of an experiment. Example: Rolling a die; you could get a 1,2,3,4,5, or 6. Those are your possible events. Example: Rolling a die and tossing a coin; you could get a 3 and heads, that is an example of an event. Outcome - A possible result of a probability experiment is called an outcome. Example: Head is a possible outcome when a coin is tossed.

5. Sample Problem #1 Morgan rolls a die twice. What is the probability she gets a two both times? Is this event dependent or independent? Does one event affect the outcome of the other?

6. Solution to Problem #1 This event is independent because the roll of a die one time does not affect the roll of a die the next time. Therefore, the first chance is 1 out of 6 and the second chance is 1 out of 6. So the probability of rolling a two both times is: 1/6 x 1/6 = 1/36

7. Sample Problem #2 A deck of cards has 5 yellow, 3 violet, 3 purple, 4 blue, and 5 pink cards. You pick 2 cards from the deck. Cards are not returned to the deck after they are picked. What is the P(the first card is purple and the second card is pink)? Is this event dependent or independent? Does one event affect the outcome of the other?

8. Solution to Problem #2 This event is dependent because one event is affected by the outcome of the other event. Also we know by the word not returned. First we need to know how many cards there are 5 yellow + 3 violet + 3 purple + 4 blue + 5 pink = 20 cards P(the first card is purple and the second card is pink) 3 purple out of 20 cards, then 5 pink out of 19 cards 3/20 x 5/19 = 15/380 = 3/76

9. Sample Problem #3 There are 6 red, 6 black, and 6 gray marbles in a hat. You pick 3 marbles from the hat. Marbles are not returned after they have been drawn. What is the P(three gray marbles in a row)? Is this event dependent or independent? Does one event affect the outcome of the other?

10. Solution to Problem #3 This event is dependent because one event is affected by the outcome of the other event. Also we know by the word not returned. First we need to know how many marbles there are 6 red + 6 black + 6 gray = 18 marbles. P(three gray marbles in a row) 6 gray out of 18, then 5 gray out of 17, then 4 gray out of 16. 6/18 x 5/17 x 4/16 = 120/4896 = 5/204

11. How to complete the assignment Paste each independent question here Paste each dependent question here Name Name

12. Answer Sheet You need to pick 6 problems from the dependent sheet and 6 from the independent sheet and answer them. Show the fractions you are multiplying together for each problem on your answer sheet. Finally answer the story problems and short answer ?

13. When is it due? This whole assignment : both dependent & independent sheets, the answer sheet with 12 problems, and the story problems are due: MONDAY, March 21st! If you need to go back and review how to do the problems and listen to my explanations again you can go to: Mrsbrach.wikispaces.com Click on the Math link on the left hand side and scroll down to Dependent and Independent Events PowerPoint 