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Gain Confidence with Probability: The Two-Way Table
1-19.
AN ASSOCIATION?
The Collectable Card Club wants to take a trip to their State’s Card-a-Con. Tonya is
trying to gather information to order club t-shirts in either male or female cuts, and
arrange carpools, so she takes a census of the club’s members.
31 males, 9 females, 13 members with cars, 27 without cars. She also notices that
only one-third of the girls have cars.
3-31.
a.
Use her census information to make an appropriate chart or graph.
b.
Tonya is convinced there is a relationship between the variables ‘gender’ and
‘having a car.’ Do you agree with Tonya? Justify your reasoning.
In Canada, 92% of the households have televisions. 72% of households have
televisions and Internet access. 5% have neither.
a.
Create a relative frequency table of this situation.
b.
What is the probability of selecting a Canadian house at random that has
Internet access but no television?
c.
What is the conditional probability of selecting a house that has Internet given
that it has a television?
d.
Of the houses that do not have television, what is the conditional probability of
selecting one that has Internet access?
e.
Is there an association between television ownership and Internet access in
Canadian homes. Provide evidence.
© 2013 CPM Educational Program. All rights reserved
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Gain Confidence with Probability: The Two-Way Table
3-27.
APPLES AND BANANAS
Let event “A” represent a randomly selected high
school student ate an apple at lunch and event “B”
represent the student ate a banana at lunch. The
event did NOT eat an apple is then A and did
NOT eat a banana is B .
B
B
A
0.20
0.10
0.30
A
0.45
0.25
0.70
0.65
0.35
The right notation can save a lot of explaining.
For example, answer each of the next two questions in a complete sentence:
a.
P(B) = ______
b.
P( A ) = ______
The symbol  stands for the “union” and represent the “or” condition, while the
symbol  stands for “intersection” and represents the “and” condition. Often the
symbol “ | ” is used to represent “given that”. P(G | H) represents the probability of
G given that H has occurred.
Convert the following language to probability notation and find the probabilities
associated with randomly selecting a high school student who
c.
ate a banana and an apple at lunch.
d.
ate a banana or did not eat an apple at lunch.
e.
did not eat a banana and ate an apple at lunch.
f.
ate a banana given that they ate an apple at lunch.
B
Here is the Apples and Bananas table
with the relative frequencies
removed. Some of the relative
frequencies have been replaced with
their associated probability notations.
g.
B
A
P(A)
P( A ∩ B )
A
P(B)
Fill in the other missing relative
frequencies with the correct probability notation.
© 2013 CPM Educational Program. All rights reserved
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Gain Confidence with Probability: The Two-Way Table
3-30.
Here is the Apples and Bananas table
again with all of the relative frequencies
removed and replaced with their
associated probability notations.
B
B
A
P(A  B)
P(A  B )
P(A)
A
P( A  B)
P( A ∩ B )
P( A )
P(B)
P( B )
Using only probability notation, (no
numbers) create expressions which
represent the events shown in parts (a)
through (d). Do not use the A or B symbols.
3-39.
a.
P(B | A) =
b.
P(A | B) =
c.
P(A  B) =
d.
Now consider a case where you were given a conditional probability such as
P(A | B) along with P(B). Show symbolically how you could get the joint
probability P(A  B).
Of the students who choose to live on the East Coast College campus, 10% are
seniors. The most desirable dorm is the newly constructed Ocean View dorm, and
60% of the seniors who live on campus live there, while 20% of the rest of the oncampus students live there.
a.
Represent these probabilities in a graphical display (tree, and/or relative
frequency table).
b.
What is the probability that a randomly selected resident of the Ocean View
dorm is a senior?
© 2013 CPM Educational Program. All rights reserved
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Gain Confidence with Probability: The Two-Way Table
5-21.
Governments and security companies are coming to rely more heavily on facial
recognition software to locate persons of interest.
Consider a hypothetical situation. Suppose that facial recognition software can
accurately identify a person 99.9% of the time, and suppose the suspect is among
200,000 facial images available to a government agency. When the software makes a
positive identification, what it the probability that it is not the suspect?
9-26.
a.
Make a two-way table for this situation.
b.
If a person has been identified as the suspect, what is the probability that he or
she is not actually the suspect?
People of Madelinton are security-conscious and have sophisticated car alarms
installed on their cars. Over the course of a year these alarms correctly
distinguish between a break-in attempt and other harmless events at a 99%
rate. Of the 820,600 cars in Madelinton about 100 are broken into each year. If a
citizen of Madelinton hears a car alarm, what is the probability the car is being
broken into
https://ebooks.cpm.org/apstat/ap_stats_problem_gen_v1.0/index.html
© 2013 CPM Educational Program. All rights reserved
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