Problem 3:
A box contains 10 balls of the following types:
3 are red and dotted
2 are gray and dotted
1 is red and striped
4 are gray and striped
If you randomly select one ball, what is the probability that the ball is
(a)
dotted?
(b)
dotted, given that it is red?
(c)
dotted or red?
Problem 4:
Among the patients at a mental health clinic, 35% suffer from depression and 40% suffer from anxiety.
A total
of 28% of the patients suffer from both conditions.
(a)
Display this information in a Venn diagram.
Use your Venn Diagram to determine what percent of the patients at this clinic ….
(a)
…suffer from depression but not anxiety.
________
(b)
…suffer from neither depression nor anxiety. _____
Problem 5:
Two socks are selected at random and removed in succession (without replacement) from a drawer containing 6
brown socks and 4 blue socks.
Let
Y
represent the number of brown socks selected.
Give the probability distribution for
Y
:
Y
=
Probability =
Support your probabilities by a well labeled tree diagram to the right:
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Chapter 6:
Probability and Simulation: The Study of Randomness
Problem 6:
The probability that a particular type of smoke detector will function properly and sound an alarm in the presence
of smoke is 0.9.
If there are two of these alarms in my home, what is the probability that at least one works in the presence of
smoke?
Problem 7:
A manufacturer of airplane parts knows from past experience that the probability is 0.8 that an order will be
ready for shipment on time, the probability is 0.6 that an order will be delivered on time, and the probability is 0.5 that an
order will be ready for shipment
and
will be delivered on time.
(a) Find the probability that an order will be delivered on time, given that it is ready for shipment on time.
(b) Find the probability that a randomly selected order will be ready for shipment on time or will be delivered on time.
Problem 8:
A box contains 20 fuses, 17 good and 3 defective.
Two fuses are drawn from the box
with replacement
.
(a)
What is the probability that both fuses are defective?
(b)
What is the probability that one fuse is good and one is defective?
Problem 9:
A recent survey asked 100 randomly selected adult Americans if they thought that women should be allowed to
go into combat situations.
Here are the results:
Gender
Yes
No
Male
32
18
Female
8
42
(a)
Find the probability of a “Yes” answer, given that the person was a female.
(b)
Find the probability that the respondent was a male, given that the response was a “No.”
Problem 10:
Toss two balanced coins.
Let A = head on the first toss, and let B = both tosses have the same outcome.
Are
events A and B independent?
Explain your reasoning clearly.
Problem 11:
Parking for students at Central High School is very limited, and those who arrive late have to park illegally and
take their chances at getting a ticket.
Joey has determined that the probability that he has to park illegally and that he gets a
parking ticket is 0.07.
He recorded data last year and found that because of his perpetual tardiness, the probability that he
will have to park illegally is 0.25.
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 Fall '12
 SonjaCox
 Probability, AP Statistics, Probability theory, Randomness, The Study of Randomness

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