Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Material Type: Exam; Class: Elementary Probability & Statistics; Subject: Mathematics; University: Pellissippi State Technical Community College; Term: Unknown 1989;
Typology: Exams
1 / 11
This page cannot be seen from the preview
Don't miss anything!
Tree Diagram of Test Answers
a b c d e a b c d e
Tree Diagram of Test Answers
TaTbTcTdTeFaFbFcFdFe
a b c d e a b c d e
Tree Diagram of Test Answers
TaTbTcTdTeFaFbFcFdFe
a b c d e a b c d e
Tree Diagram of Test Answers
TaTbTcTdTeFaFbFcFdFe
a b c d e a b c d e
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) =
Independent Events
Two selections
With replacement
P (both good) =
P (good and good) =
=
= 0.
Two selections
Without replacement
P (both good) =
Two selections
Without replacement
P (both good) =
P (good) and P(good) =
Two selections
Without replacement
P (both good) =
P (good)
P(good) =
Two selections
Without replacement
P (both good) =
P (good)
P(good) =
Intuitive Multiplication
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.
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:
P(all 4 cars stolen ) = P(stolen) P(stolen) P(stolen) P(stolen)=
Example:
P(all 4 cars stolen ) = P(stolen) P(stolen) P(stolen) P(stolen)=INDEPENDENT 43650
4
(
)
Example:
P(all 4 cars stolen ) = P(stolen) P(stolen) P(stolen) P(stolen)=INDEPENDENT
4
=
Example:
P(all 4 cars stolen ) = P(stolen) P(stolen) P(stolen) P(stolen)=INDEPENDENT
4
=
Independence
You must treat a problem as
independent when:
you do not have the sample orpopulation size, and
you have only a percentage(probability) of the individualcharacteristic
