Section 4 3
This presentation is the property of its rightful owner.
Sponsored Links
1 / 15

Section 4-3 PowerPoint PPT Presentation


  • 42 Views
  • Uploaded on
  • Presentation posted in: General

Section 4-3. The Addition Rule. COMPOUND EVENT. A compound event is any event combining two or more simple events. NOTATION P ( A or B ) = P (in a single trial, event A occurs or event B occurs or they both occur).

Download Presentation

Section 4-3

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Section 4 3

Section 4-3

The Addition Rule


Compound event

COMPOUND EVENT

A compound event is any event combining two or more simple events.

NOTATION

P(A or B) = P(in a single trial, event A occurs or event B occurs or they both occur)


General rule for finding the probability of a compound event

GENERAL RULE FOR FINDING THE PROBABILITY OF 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.


Formal addition rule

FORMAL ADDITION RULE

where P(A and B) denotes the probability that A and B both occur at the same time as an outcome in a trial of a procedure.


Intuitive addition rule

INTUITIVE ADDITION RULE

To find P(A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, adding in such a way that every outcome is counted only once. P(A or B) is equal to that sum, divided by the total number of outcomes in the sample space.


Disjoint events

DISJOINT EVENTS

Events A and B are disjoint (or mutually exclusive) if they cannot both occur together.


Observations on disjoint events

OBSERVATIONS ONDISJOINT EVENTS

  • If two events, A and B, are disjoint, then P(A and B) = 0.

  • If events A and B are disjoint, then

    P(A or B) = P(A) + P(B).


Applying the addition rule

APPLYING THE ADDITION RULE

P(A or B)

Addition Rule

Are

A and B

disjoint

?

Yes

P(A or B) = P(A) + P(B)

Disjoint events cannot happen at the same time. They are separate, nonoverlapping events.

No

P(A or B) = P(A) + P(B) −P(A and B)


Example

EXAMPLE

The data in the chart below represent the marital status of males and females 18 years or older in the US in 1998. Use it to answer the questions on the next slide.


Example concluded

EXAMPLE (CONCLUDED)

  • Determine the probability that a randomly selected United States resident 18 years or older is male.

  • Determine the probability that a randomly selected United States resident 18 years or older is widowed.

  • Determine the probability that a randomly selected United States resident 18 years or older is widowed or divorced.

  • Determine the probability that a randomly selected United States resident 18 years or older is male or widowed.


Complementary events

COMPLEMENTARY EVENTS

Note that events A and are disjoint. Also, we can be absolutely certain that either A or occurs. So we have


Rule of complementary events

RULE OF COMPLEMENTARY EVENTS


Venn diagram for the complement of a

VENN DIAGRAM FOR THE COMPLEMENT OF A


Example1

EXAMPLE

The data in the table below represent the income distribution of households in the US in 2000. (Source: US Bureau of the Census)


Example concluded1

EXAMPLE (CONCLUDED)

  • Compute the probability that a randomly selected household earned $200,000 or more in 2000.

  • Compute the probability that a randomly selected household earned less than $200,000 in 2000.

  • Compute the probability that a randomly selected household earned at least $10,000 in 2000.


  • Login