1 / 7

Complements, Disjoint Events, and the Addition Rule

Complements, Disjoint Events, and the Addition Rule. Presentation 4.3 Overview. Probability Rules. The probability P(A) of any event is always a number between 0 and 1. The probability that you can read this is 1 (since we know for a fact you are reading it right now).

sissy
Télécharger la présentation

Complements, Disjoint Events, and the 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. Complements, Disjoint Events, and the Addition Rule Presentation 4.3 Overview

  2. Probability Rules • The probability P(A) of any event is always a number between 0 and 1. • The probability that you can read this is 1 (since we know for a fact you are reading it right now). • The probability that the Jupiter is currently closer to the sun than Earth is 0 (it simply is not true). • The probability that you will be struck by lightning are 1/709260 or 0.0000014, rather close to 0. • According to Star Wars, the probability of successfully navigating an asteroid field are 1/3720 or 0.00027.

  3. Probability Rules • If S is the sample space in a probability model, the P(S) = 1. • That is, the probability that you get something from the sample space is 1, meaning it will happen. • This comes to you from the department of redundancy department.

  4. Probability Rules • The complement of any event A is the probability that the event A will NOT occur. • If the probability that it will snow today is 40%, then the probability that it will not snow is 60%.

  5. Probability Rules • Two events are disjoint (also called mutually exclusive) if they have no outcomes in common. • Examples from a Deck of Cards • Event A is choosing a face card and event B is choosing a 5. There is no way to choose a face card that is also a 5. These are disjoint or mutually exclusive. • Event A is choosing a 5 and event B is choosing a spade. Since there is a 5 of spades (an outcome in A and B) these are NOT disjoint or mutually exclusive.

  6. Probability Rules • Addition Rule • If A and B are disjoint (mutually exclusive), then: • P(A or B) = P(A) + P(B) • Example • What is the probability or choosing a 5 or a face card? • The probability of choosing a 5 is 4/52 since there are 4 fives in the deck of 52 cards. • The probability of choosing a face card is 12/52 since there are 12 face cards (J, Q, K in each of four suits) in the deck of 52. • Since they are mutually exclusive, • The probability is 4/52 + 12/52 = 16/52 or 0.3077.

  7. Complements, Disjoint Events, and the Addition Rule • This concludes this presentation.

More Related