1 / 13

Section 5.2 The Addition Rule and Complements

Section 5.2 The Addition Rule and Complements. KEY IDEA All disjoint events in a sample space sum to 1. Two events are disjoint if they have no outcomes in common. Disjoint events are also called mutually exclusive events. Example: Toss a coin. H and T are disjoint.

dominy
Download Presentation

Section 5.2 The Addition Rule and Complements

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. Section 5.2The Addition Rule and Complements

  2. KEY IDEA All disjoint events in a sample space sum to 1

  3. Two events are disjoint if they have no outcomes in common. • Disjoint events are also called mutually exclusive events. • Example: Toss a coin. H and T are disjoint. • Example: Roll a die. 1,2,3,4,5,6 are disjoint. • Example: Roll a die. The events E={1,2,3} and F={4,5,6} are disjoint. • Example: Roll a die. The events E={1,2,3} and F={2,4,6} are not disjoint. They share {2}.

  4. Venn Diagrams Used to display simple probability logic. But requires special software to draw on computer.

  5. Let S=sample space={1,2,3,4,5,6,7,8,9,10} A={1,2,3,4,10), B={4,5,6,7,9}

  6. “Union of A and B” = A or B = A U B = { 1, 2, 3, 4, 5, 6, 7, 9, 10 } “Intersection of A and B” = A and B = A ∩ B = { 4 } “Not A” = complement of A = AC = {5, 6, 7, 8, 9}

  7. Addition Rule for Disjoint Events P(A or B) = P(A U B) = P(A) + P(B) IF A and B are disjoint events

  8. For non-disjoint and disjoint events P(A U B) = P(A) + P(B) – P(A∩B) Notice 1: P(A)+P(B) counts intersection twice. Notice 2: If A and B are disjoint, P(A∩B)=0.

  9. Complement Rule P(AC)=1-P(A)

  10. Show P(A U B) = P(A) + P(B) – P(A∩B)

  11. P(A and C) = ? P(A or C ) = ? P(A and B) = ? P(A or B) = ? P(A or B or C)=?

  12. From a 52 card deck, what is P( Spades or King)?

More Related