1 / 17

Understanding Probability: Concepts, Laws, and Applications in Data Interpretation

This lecture explores the fundamental concept of probability, focusing on its definitions, laws, and practical applications. Key objectives include explaining probability, using tree diagrams, and constructing probability tables. Topics covered include subjective, empirical, and a priori probabilities, as well as independent, mutually exclusive, and mutually exhaustive events. The lecture delves into the special laws of addition and joint probability with practical examples, guiding learners through real-world applications like card drawing and machine reliability assessments.

afrodite-ballas
Télécharger la présentation

Understanding Probability: Concepts, Laws, and Applications in Data Interpretation

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. LBSRE1021 Data Interpretation Lecture 4 Probability

  2. Objectives • Explain the concept of probability • Apply simple laws of probability • Construct and use a tree diagram • Construct and use a probability table

  3. Probability Scale

  4. How is a probability determined? (1) 1. Subjective- estimate by experience 2. Empirical- by measurement p = No. times event occurred Total number of trials Affected by sampling error. E.g. toss a coin a number of times Is probability of heads 0.5?

  5. How is a probability determined? (2) 3. A Priori Work out in advance Requires knowledge Assumes all outcomes equally likely e.g. probability of head 0.5 ace from pack of 52 cards 4/52 p= No. ways an event can occur Total number of possible outcomes

  6. Pack of Cards • 52 cards in pack • Divided into 4 ‘suits’ • Clubs, Diamonds, Hearts, Spades • 13 cards in each suit • Ace,2,3,4,5,6,7,8,9,10, Jack, Queen, King

  7. Compound Events (1) • Events Can be: • Independent: occurrence of one does not affect the other • Mutually Exclusive: either can occur but not both • e.g. one card cannot be both Q and A • Q and Heart not Mutually Exclusive

  8. Compound Events (2) • Mutually Exhaustive: set of all possible outcomes known • The sum of the probabilities of a set of outcomes which are mutually exhaustive and mutually exclusive =1

  9. Laws of Probability Special Law of Addition. Two events E1 and E2, The probability that either E1 occurs or E2 occurs is P(E1 or E2) = P(E1) + P(E2) Provided that E1 and E2 are mutually exclusive

  10. Special Law of Addition Example draw a card from a pack E1 = card is a heart, P(E1) = 1/4 E2 = card is a diamond P(E2) = 1/4 P(E1 or E2) = 1/4 + 1/4 = 1/2

  11. Joint Probability For two events E1 and E2, the probability they both occur is: P(E1 and E2) = P(E1) x P(E2) Provided the events are independent I.e. the outcome of E1 does not affect the outcome of E2

  12. Joint Probability Example Draw card from pack E1 = card is a heart P(E1) = 1/4 E2 = card is an ace P(E2) = 1/13 P(E1 and E2) = 1/4 x 1/13 = 1/52 I.e. card is ace of hearts. If events are independent they cannot be mutually exclusive

  13. Tree Diagrams • The probability that machine A and machine B are still functioning in 5 year's time is 0.25 and 0.4 respectively. • Find the probability that in 5 year's time • (a) both are working • (b) neither works • (c) at least one machine works • (d) just one machine is working

  14. Tree Diagram Example

  15. Tabular Data (1)

  16. Tabular Data (2) Driver randomly selected. Find the probability that s/he (a) changed to a smaller car 47 + 22 + 69 = 0.276 500 (b) changed to a larger car 36 + 11 + 63 = 0.22 500

  17. Tabular Data (3) (c) bought a large car, given that he previously had a small or medium car. 36 + 11 = 0.132 180 + 176

More Related