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Quiz 10
Question 1
Let A and B be events in a sample space S such that P(A) = 0.34, P(B) = 0.39 and P(A ∩ B) = 0.19.
Find P(A | B).
a)
0.4872
b)
0.5588
c)
0.0256
d)
0.2603
e)
0.8718
f)
None of the above.
Question 2
Let A and B be events in a sample space S such that P(A) = 21⁄100 , P(B) = 47⁄100 , and P(A ∩ B) = 2⁄25 .
Find P(B | Ac ).
Hint: Draw a Venn Diagram to find P(Ac ∩ B).
a)
0.5949
b)
0.1013
c)
0.8298
d)
2.2381
e)
0.4937
f)
None of the above.
Question 3
Suppose that A and B are independent events. If P(A) = 1⁄5 and P(B) = 7⁄10 , find P(A ∩ B).
a)
0.02
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b)
1.00
c)
0.07
d)
0.09
e)
0.14
f)
None of the above.
Question 4
Quality Control: A company has four photocopy machines A, B, C and D. The probability that a given
machine will break down on a particular day is
P(A) = 7⁄50
P(B) = 4⁄25
P(C) = 3⁄20
P(D) = 11⁄100
Assuming independence, what is the probability on a particular day that all machines will break down?
a)
0.00000224
b)
0.00036960
c)
0.01000000
d)
0.27056277
e)
0.00270563
f)
None of the above.
Question 5
A pair of fair dice is cast. What is the probabiliy that one of the numbers falling uppermost is a 5, given
that the two numbers falling uppermost are different?
a)
0.2778
b)
0.9091
c)
0.3667
d)
0.3333
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e)
0.3056
f)
None of the above.
Question 6
Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the
probability that the first card drawn is a Diamond and the second card drawn is not a Diamond?
a)
0.1875
b)
0.1912
c)
0.0577
d)
0.0588
e)
0.7500
f)
None of the above.
Question 7
Suppose we have two urns, Urn 1 and Urn 2. Urn 1 contains 3 red marbles and 5 white marbles. Urn 2
contains 9 red marbles and 11 white marbles. The experiment consists of first choosing an urn with
equally likely probability, and then drawing a marble from that urn. What is the probability of choosing
Urn 2 and a red marble?
a)
0.5500
b)
0.2250
c)
0.3125
d)
0.3750
e)
0.1875
f)
None of the above.
Question 8
A recording company obtains the blank CDs used to produce its labels from three compact disk
manufacturers: I, II, and III. The quality control department of the company has determined that 7% of
the compact disks produced by manufacturer I are defective, 5% of those produced by manufacturer II
are defective, and 4% of those produced by manufacturer III are defective. Manufacturers I, II, and III
supply 37%, 45%, and 18%, respectively, of the compact disks used by the company. What is the
probability that a randomly selected label produced by the company will contain a defective compact
disk?
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a)
0.0259
b)
0.0072
c)
0.0556
d)
0.0225
e)
0.1600
f)
None of the above.
Question 9
Suppose that 8 green balls and 14 purple balls are placed in an urn. Two balls are then drawn in
succession. What is the probability that the second ball drawn is a purple ball if the first ball is replaced
before the second is drawn?
a)
0.7273
b)
0.3636
c)
0.6818
d)
0.1122
e)
0.6364
f)
None of the above.
Question 10
Suppose that 6 green balls and 9 purple balls are placed in an urn. Two balls are then drawn in succession.
What is the probability that both balls drawn have the same color if the first ball is replaced before the
second is drawn?
a)
0.0800
b)
0.2400
c)
0.1600
d)
0.5200
e)
0.3600
f)
None of the above.
Question 11
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Seniors at a certain high school took a survey regarding future plans. All plan to attend college some time;
however, 76% plan to go to college immediately following high school. Of those who plan to attend
college immediately following high school, 17% plan to major in Math. Of those who do not plan to
attend college immediately following high school, 11% plan to major in Math. What is the probability that
a randomly chosen senior does not plan to attend college immediately following high school and plans to
major in Math.
a)
0.1100
b)
0.8900
c)
0.0264
d)
0.1292
e)
0.1700
f)
None of the above.
Question 12
A new test to detect TB has been designed. It is estimated that 87% of people taking this test have the
disease. The test detects the disease in 97% of those who have the disease. The test does not detect the
disease in 98% of those who do not have the disease. If a person taking the test is chosen at random, what
is the probability of the test indicating that the person does not have the disease?
a)
0.0261
b)
0.0200
c)
0.1535
d)
0.9800
e)
0.0300
f)
None of the above.
Question 13
Urn A contains 12 yellow balls and 4 red balls. Urn B contains 6 yellow balls and 9 red balls. Urn C
contains 10 yellow balls and 3 red balls. An urn is picked randomly (assume that each urn is equally likely
to be chosen), and then a ball is picked from the selected urn. What is the probability that the chosen ball
came from urn B, given that it was a yellow ball?
a)
0.4008
b)
0.2084
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c)
0.0685
d)
0.0711
e)
0.3908
f)
None of the above.
Question 14
11 yellow balls and 14 red balls are placed in an urn. Two balls are then drawn in succession without
replacement. What is the probability that the first ball drawn is a red ball if the second ball drawn is
yellow?
a)
0.9167
b)
0.6000
c)
0.5833
d)
0.1276
e)
0.4400
f)
None of the above.
Question 15
An arcade booth at a county fair has a person pick a coin from two possible coins available and then toss
it. If the coin chosen lands on heads, the person gets a prize. One coin is a fair coin and one coin is a
biased coin (unfair) with only a 37% chance of getting a head. Assuming equally likely probability of
picking either coin, what is the probability that the fair coin is the one chosen, given that the chosen coin
lands on heads?
a)
0.4032
b)
0.5747
c)
0.0133
d)
0.8700
e)
0.4350
f)
None of the above.
Question 16
King Mattress purchases Sleep-n-Air mattresses from three different distributors. The probability of
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getting a defective mattress from Distributor A, B, or C is 0.18, 0.12, and 0.54, respectively. Assume an
equal probability of making a purchase from each distributor A, B, or C. If King Mattress sells a defective
mattress, what is the probability that it came from Distributor A?
a)
0.1429
b)
0.1667
c)
0.2500
d)
0.2143
e)
0.6429
f)
None of the above.
Question 17
There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar
contains 10 chocolate chip and 7 sugar cookies. The green jar contains 8 chocolate chip, 14 sugar and 11
peanut butter cookies. The pink jar contains 6 chocolate chip, 5 sugar and 9 peanut butter cookies. One
of the three cookie jars is chosen at random. The probabilities that the blue jar, green jar, or pink jar will
be chosen are 1⁄2 , 1⁄4 , and 1⁄4 , respectively. A cookie is then chosen at random from the chosen jar.
What is the probability that the pink jar was chosen, if it is known that the cookie was a sugar cookie?
a)
0.0833
b)
0.2302
c)
0.0625
d)
0.1669
e)
0.2500
f)
None of the above.
Question 18
An experiment consists of choosing an urn with the following probabilities that Urn 1, Urn 2, or Urn 3 will
be chosen: 1/2, 1/4, and 1/4, respectively. Urn 1 contains 15 brown marbles and 14 clear marbles. Urn 2
contains 6 brown marbles, 11 clear marbles and 9 red marbles. Urn 3 contains 7 brown marbles, 8 clear
marbles and 5 red marbles.
A marble is then chosen from the chosen urn. What is the probability that Urn 3 was chosen, given that
the marble chosen was clear?
a)
0.1000
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b)
0.4000
c)
0.1333
d)
0.3063
e)
0.2236
f)
None of the above.
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