Another name for disjoint events is
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1 Name: Date: Hour: Unit 6 Disjoint Events By the end of this lesson, you will be able to Use the Addition Rule for disjoint events Disjoint Events: Another name for disjoint events is It is often helpful to draw pictures of events. These pictures are called Venn Diagrams, which are represented as circles enclosed in a rectangle. The rectangle represents the sample space, and each circle represents an event. Example 1: Suppose we randomly select chips from a bag. Each chip is labeled 0-9. Let E represent the event choose a number less than or equal to 2. Let F represent the event choose a number greater than or equal to 8. Fill in the Venn diagram above using this information. **FOR DISJOINT/MUTUALLY EXCLUSIVE EVENTS, the Addition Rule for Disjoint events Example 2: Suppose a single card is selected from a standard deck of 52 cards. (a) Compute the probability of the event E = drawing a Jack (b) Compute the probability of the event E = drawing a Jack or F = drawing a 5. (c) Compute P(drawing a king or drawing a queen or drawing a jack)
2 Example 3: A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green marbles. A marble is selected from the bag a. What is the probability that the marble is white or blue? b. Determine P(red or yellow) c. Determine P(not green) Example 4: Lunch Tacos.09 Meatball sub.35 Pizza.26 Fish.18 Chicken strips.12 a. Determine the probability of having tacos at lunch. b. Find P(meatball sub or pizza) c. Find P(pizza or chicken strips or fish)
3 Quick Check Disjoint Events Self Assessment 1. What does it mean when two events are disjoint? 2. If E and F are two disjoint events, the P(E or F) = 3. Event E = rolling an even number and event F = rolling a 5 a. Are the two events mutually exclusive? b. Calculate P(E) then P(F) separately. c. Calculate P(E or F). Learning Goals Use the Addition Rule for disjoint events Self-Assessment I am unsure of or confused about this I am ready to start practicing I am already good at this My Goals for Today- thinking about what I am good at, where am I confused and what do I need to work on? What do I do if I am confused or need to work on a learning target?
4 Name: Date: Hour: Unit 6 Disjoint Events Homework In the following problems, a probability experiment is conducted in which the sample space of the experiment is S = {1,2,3,4,5,6,7,8,9,10,11,12}. Let event E={2,3,4,5,6,7}, event F={5,6,7,8,9}, event G={9,10,11,12}, and event H={2,3,4}. Assume each outcome is equally likely. 1. List the outcomes that are in both E and F. Are E and F mutually exclusive? 2. List the outcomes that are in F or G. Are F and G disjoint? 3. List the outcomes of E and G. Are E and G mutually exclusive? 4. Calculate P(E or G). For the following problems, a golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleists, 8 Maxflis, and 3 Top-Flites, find the probability of each event. 5. P(Titleist) 6. P(Maxfli) 7. P(Top-Flite) 8. P(Titleist or Maxfli) 9. P(NOT a Titleist) 10. P(Maxfli or Top-Flite) 11. P(NOT a Top-Flite)
5 12. The following model shows the distribution of doctoral degrees from US universities in 2003 by area of study. Area of Study Engineering Physical Sciences Life Sciences Mathematics Computer Sciences Social Sciences Humanities Education Professional and Other Fields a. Verify that this is a probability model. b. What is the probability that a randomly selected doctoral candidate who earned a degree in 2003 studied physical science or life science? c. What is the probability that a randomly selected doctoral candidate who earned a degree in 2003 studied physical science, life science, mathematics, or computer science? d. What is the probability that a randomly selected doctoral candidate who earned a degree in 2003 did not study mathematics? e. Which degree is the least likely? Which is the most likely? How do you know?
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