1 / 18

Addition Rule

Addition Rule. Definition. Compound Event Any event combining 2 or more simple events. Notation P ( A or B ) = P (event A occurs or event B occurs or A and B both occur). General Rule for a Compound Event.

shona
Download Presentation

Addition Rule

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. Addition Rule

  2. Definition • Compound Event • Any event combining 2 or more simple events Notation P(A or B) = P (event A occurs or event B occurs or A and B both occur)

  3. General Rule for a Compound Event • When finding the probability that event A occurs or event B occurs, find the total number of ways A can occur and the number of ways B can occur, but find the total in such a way that no outcome is counted more than once. • To count each outcome only once, we first need to understand the term mutually exclusive or disjoint.

  4. Mutually Exclusive Events A and B A B A B Two events, A and B, are mutually exclusive, also know as disjoint, if they cannot occur at the same time. A and B are mutually exclusive. A and B are not mutually exclusive.

  5. Mutually Exclusive Events A B 1 2 4 Example: Decide if the two events are mutually exclusive (disjoint). Event A: Roll a number less than 3 on a die. Event B: Roll a 4 on a die. These events cannot happen at the same time, so the events are mutually exclusive or disjoint.

  6. Mutually Exclusive Events A B 2 9 J 10 3 A 7 J J K 4 5 J 8 6 Q Example: Decide if the two events are mutually exclusive (disjoint). Event A: Select a Jack from a deck of cards. Event B: Select a heart from a deck of cards. Because the card can be a Jack and a heart at the same time, the events are not mutually exclusive.

  7. A deck of cards

  8. The Addition Rule The probability that event A or B will occur is given by P (A or B) = P (A) + P (B) – P (A and B ). If events A and B are mutually exclusive, then the rule can be simplified to P (A or B) = P (A) + P (B). Example: You roll a die. Find the probability that you roll a number less than 3 or a 4. The events are mutually exclusive. P (roll a number less than 3 or roll a 4) = P (number is less than 3) + P (4)

  9. Applying the Addition Rule Figure 3-6

  10. The Addition Rule Example: A card is randomly selected from a deck of cards. Find the probability that the card is a Jack or the card is a heart. The events are not mutually exclusive because the Jack of hearts can occur in both events. P (select a Jack or select a heart) = P (Jack) + P (heart) – P (Jack of hearts)

  11. The Addition Rule Example: 100 college students were surveyed and asked how many hours a week they spent studying. The results are in the table below. Find the probability that a student spends between 5 and 10 hours or more than 10 hours studying. The events are mutually exclusive. P (5 to10) + P (10) P (5 to10 hours or more than 10 hours) =

  12. Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 Example Titanic Passengers • Find the probability of randomly selecting a man or a boy.

  13. Example Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 • Find the probability of randomly selecting a man or a boy. • P (man or boy) = * Disjoint (Mutally Exclusive) *

  14. Example Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 • Find the probability of randomly selecting a man or • someone who survived.

  15. Example Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 • Find the probability of randomly selecting a man or someone who survived. • P(man or survivor) = * NOT Mutally Exclusive (Disjoint)*

  16. Complementary Events All simple events are either in A or A. • A and A • are • mutually exclusive

  17. Rules of Complementary Events P(A) + P(A) = 1 = 1 –P(A) P(A) = 1 –P(A) P(A)

  18. Venn Diagram for the Complement of Event A Figure 3-7

More Related