Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Multiplication Rule: Basics - Lecture Slides | MATH 1530, Exams of Probability and Statistics

Material Type: Exam; Class: Elementary Probability & Statistics; Subject: Mathematics; University: Pellissippi State Technical Community College; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

koofers-user-bzr-1
koofers-user-bzr-1 🇺🇸

10 documents

1 / 11

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
3 - 4
Multiplication Rule:
Basics
Finding the Probability of
Two or More Selections
Multiple selections
Multiplication Rule
Notation
P(A and B) =
P(event A occurs in a first trial and
event B occurs in a second trial)
T
F
Tree Diagram of Test Answers
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Multiplication Rule: Basics - Lecture Slides | MATH 1530 and more Exams Probability and Statistics in PDF only on Docsity!

Multiplication Rule:

Basics

Finding the Probability of

Two or More Selections

Multiple selections

Multiplication Rule

Notation

P(A and B) =P(event A occurs in a first trial and

event B occurs in a second trial)

T F

Tree Diagram of Test Answers

a b c d e a b c d e

T F

Tree Diagram of Test Answers

TaTbTcTdTeFaFbFcFdFe

a b c d e a b c d e

T F

Tree Diagram of Test Answers

TaTbTcTdTeFaFbFcFdFe

a b c d e a b c d e

T F

Tree Diagram of Test Answers

TaTbTcTdTeFaFbFcFdFe

a b c d e a b c d e

T F

P(T) =

P(c) =

P(T and c) =

Tree Diagram of Test Answers

1 2

1 5

1 10

™

P(A and B) = P(A) • P(B A)

™

If A and B are independent events,

P(B A) is really the same as P(B)

Formal Multiplication Rule

Applying the Multiplication Rule

P(A and B)

Multiplication Rule

Are

A and B

independent

?

P(A and B) = P(A) • P(B A)

P(A and B) = P(A) • P(B)

Yes

No

Independent Events

Two selections

With replacement

P (both good) =

G

G

G G

D

Independent Events

Two selections

With replacement

P (both good) =

G

G

G G

D

P (good and good) =

=

= 0.

Two selections

Without replacement

P (both good) =

G

G G

D

G

Two selections

Without replacement

P (both good) =

G

G G

D

P (good) and P(good) =

G

Two selections

Without replacement

P (both good) =

G

G G

D

P (good)

P(good) =

G

Two selections

Without replacement

P (both good) =

G

G G

D

P (good)

P(good) =

G

Intuitive Multiplication

When finding the probability that event A

occurs in one trial and B occurs in the nexttrial, multiply the probability of event A by theprobability of event B, but be sure that theprobability of event B takes into account theprevious occurrence of event A.

P(Ace on first card) =

Find the probability of drawing two cardsfrom a shuffled deck of cards such that thefirst is an Ace and the second is a King. (Thecards are drawn without replacement.)

P(Ace on first card) =

P(King Ace) =

Find the probability of drawing two cardsfrom a shuffled deck of cards such that thefirst is an Ace and the second is a King. (Thecards are drawn without replacement.)

P(Ace on first card) =

P(King Ace) =

P(drawing Ace, then a King) =

Find the probability of drawing two cardsfrom a shuffled deck of cards such that thefirst is an Ace and the second is a King. (Thecards are drawn without replacement.)

P(Ace on first card) =

P(King Ace) =

P(drawing Ace, then a King) =

Find the probability of drawing two cardsfrom a shuffled deck of cards such that thefirst is an Ace and the second is a King. (Thecards are drawn without replacement.)

DEPENDENT EVENTS

Example:

On a TV program it was reported that there

is a 60% success rate for those who try to stop smokingthrough hypnosis. Find the probability that for 8 randomlyselected smokers who undergo hypnosis, they allsuccessfully quit smoking.

Example:

On a TV program it was reported that there

is a 60% success rate for those who try to stop smokingthrough hypnosis. Find the probability that for 8 randomlyselected smokers who undergo hypnosis, they allsuccessfully quit smoking.

P(all 8 quit smoking) =

Example:

On a TV program it was reported that there

is a 60% success rate for those who try to stop smokingthrough hypnosis. Find the probability that for 8 randomlyselected smokers who undergo hypnosis, they allsuccessfully quit smoking.

P(all 8 quit smoking) =P(quit) P(quit) P(quit) P(quit) P(quit) P(quit) P(quit) P(quit) =

Example:

If Houston has an annual car-theft rate

of 4.5%, find the probability that among 4 randomlyselected cars, all are stolen during a given year.(There are 970,000 cars in Houston.)

P(all 4 cars stolen ) = P(stolen) P(stolen) P(stolen) P(stolen)=

Example:

If Houston has an annual car-theft rate

of 4.5%, find the probability that among 4 randomlyselected cars, all are stolen during a given year.(There are 970,000 cars in Houston.)

P(all 4 cars stolen ) = P(stolen) P(stolen) P(stolen) P(stolen)=INDEPENDENT 43650

4

(

)

Example:

If Houston has an annual car-theft rate

of 4.5%, find the probability that among 4 randomlyselected cars, all are stolen during a given year.(There are 970,000 cars in Houston.)

P(all 4 cars stolen ) = P(stolen) P(stolen) P(stolen) P(stolen)=INDEPENDENT

DEPENDENT

4

=

Example:

If Houston has an annual car-theft rate

of 4.5%, find the probability that among 4 randomlyselected cars, all are stolen during a given year.(There are 970,000 cars in Houston.)

P(all 4 cars stolen ) = P(stolen) P(stolen) P(stolen) P(stolen)=INDEPENDENT

DEPENDENT

4

=

Independence

You must treat a problem as

independent when:

z

you do not have the sample orpopulation size, and

z

you have only a percentage(probability) of the individualcharacteristic