1 / 10

Chapter 4: Probability (Cont.)

Chapter 4: Probability (Cont.). In this handout: Venn diagrams Event relations Laws of probability Conditional probability Independence of events. Venn Diagram: representing events graphically.

sherry
Download Presentation

Chapter 4: Probability (Cont.)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 4: Probability (Cont.) • In this handout: • Venn diagrams • Event relations • Laws of probability • Conditional probability • Independence of events

  2. Venn Diagram: representing events graphically Example: Toss a coin twice. Let event A corresponds to “ tail at the second toss ”; event B corresponds to “ at least one head ”.

  3. Example: Two monkeys to be selected by lottery for an experiment. Label the possible pairs (elementary outcomes):{1, 2} e1 {2, 3} e4{1, 3} e2 {2, 4} e5{1, 4} e3 {3, 4} e6 Let A: selected monkeys are of the same type;B: selected monkeys are of the same age;

  4. The complement of an event A is the set of all elementary outcomes that are not in A.The union of events A and B isthe set of all elementary outcomes that are in A, B, or both.The intersection of events A and B is the set of all elementary outcomes that are in A and B.

  5. Example: Equal chances that the answer to a problem is correct or wrong. What is the probability of getting at least one correct answer? P(at least one correct answer) = 1 – P(all answers wrong) = 1 – 1/8 = 7/8

  6. Conditional probability The probability of an event A must often be modified after information is obtained as to whether or not a related event B has taken place.Example: Q1: Probability that a randomly-selected person has hypertension? Q2: A randomly-selected person is overweight. What is the probability that the person also has hypertension? Let A denote “has hypertension”, B denote “overweight”. Then P(has hypertension given that overweight) = P( A | B ) = .1/.25 = .4

  7. Conditional probability Box on Page 143Conditioned probability; multiplication law of probability

  8. Independence of Events

  9. Independence of Events Example: A mechanical system consists of two components. Component 1 has reliability (probability of not failing) .98 and component 2 has reliability .95. If the system can function only if both components function, what is the reliability of the system? Let A1 denote “component 1 functions”, A2 denote “component 2 functions”, S denote “system functions”. Given that the components operate independently, we take the events A1 and A2 to be independent. Thus, P(S) = P(A1) P(A2) = .98 * .95 = .931

More Related