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