Math 1324
ExaM 3
NaME___________________________________
ChaptErs 8-9
DatE__________________________
----------------------------------------------------------------------------------------------------------------------------------------------MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana.
Alabama
soybeans (s)
peanuts (p)
corn (c)
hay (h)
wheat (w)
Arkansas
soybeans (s)
rice (r)
cotton (t)
hay (h)
wheat (w)
Louisiana
soybeans (s)
sugarcane (n)
rice (r)
corn (c)
cotton (t)
Let U be the smallest possible universal set that includes all of the crops listed; and let A, K, and L be the sets of five crops
in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.
1) L' ∩ A
1)
A) {c, s}
B) {n, r, t}
C) {h, p, w}
D) {h, n, t, w}
2) K' ∩ L
A) {c, n, p}
B) {h, w}
C) {c, n}
Decide whether the statement is true or false.
3) {5, 10, 15, 20} ∪ {5, 15} = {5, 10, 15, 20}
A) True
B) False
4) {5, 7, 9} ∩ {6, 8, 10} = {5, 7, 9, 6, 8, 10}
A) True
B) False
1
D) {r, s, t}
2)
3)
4)
Use a Venn Diagram and the given information to determine the number of elements in the indicated set.
5) n(U) = 136, n(A) = 44, n(B) = 64, n(A ∩ B) = 17, n(A ∩ C) = 20, n(A ∩ B ∩ C) = 9, n(A' ∩ B ∩ C') = 38,
and n(A' ∩ B' ∩ C') = 33. Find n(C).
A) 12
B) 28
C) 41
D) 23
5)
6) n(A) = 50, n(B) = 58, n(C) = 52, n(A ∩ B) = 10, n(A ∩ C) = 12, n(B ∩ C) = 6, n(A ∩ B ∩ C) = 4, and
n(A' ∩ B' ∩ C') = 101. Find n(U)
A) 186
B) 247
C) 136
D) 237
6)
7) n(U) = 93, n(A) = 40, n(B) = 45, n(C) = 24, n(A ∩ B) = 8, n(A ∩ C) = 6, n(B ∩ C) = 7, and
n(A ∩ (B ∩ C)) = 5. Find n(A ∩ (B ∪ C)').
A) 31
B) 1
C) 5
D) 32
7)
Use a Venn diagram to answer the question.
8) At East Zone University (EZU) there are 634 students taking College Algebra or Calculus. 516 are
taking College Algebra, 202 are taking Calculus, and 84 are taking both College Algebra and
Calculus. How many are taking Calculus but not Algebra?
A) 432
B) 348
C) 550
D) 118
8)
Use the given table to find the probability of the indicated event. Round your answer to the nearest thousandth.
9) College students were given three choices of pizza toppings and asked to choose one favorite. The
9)
following table shows the results.
toppings freshman sophomore
cheese
13
15
meat
19
25
veggie
15
13
junior
20
15
19
senior
25
13
25
A randomly selected student prefers a cheese topping.
A) .336
B) .115
C) .332
2
D) .342
Find the probability of the given event.
10) A card drawn from a well-shuffled deck of 52 cards is red.
13
1
1
A)
B)
C)
52
26
2
1
D)
52
For the experiment described, write the indicated event in set notation.
11) A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a
subset of the sample space: The second toss shows a six.
A) {(1, 6), (2, 6), (4, 6), (5, 6), (6, 6)}
B) {(3, 6)}
C) {(1, 6), (3, 6), (5, 6)}
D) {(1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6)}
10)
11)
An experiment is conducted for which the sample space is S = {a, b, c, d}. Decide if the given probability assignment is
possible for this experiment.
12)
12)
Outcomes Probabilities
a
.1
b
.2
c
.5
d
.2
A) No
B) Yes
Find the probability of the given event.
13) A bag contains 13 balls numbered 1 through 13. A randomly chosen ball has an even number.
6
2
13
A)
B)
C)
D) 6
13
13
6
3
13)
Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has two
dominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and
"hybrid" describes one who has one of each.
14) Two hybrids produce a litter of four offspring. What is the probability that none of the four is pure
14)
recessive?
A) .004
B) .75
C) .316
D) .0625
Find the odds in favor of the indicated event.
15) Spinning a D on the spinner pictured below. (The sectors are of equal size.)
A) 6 to 1
B) 1 to 7
C) 1 to 6
15)
D) 5 to 1
Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has two
dominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and
"hybrid" describes one who has one of each.
16) Two hybrids produce a litter of four offspring. What is the probability that only the first one is pure
16)
recessive?
A) .225
B) .422
C) .004
D) .105
Suppose P(C) = .048, P(M ∩ C) = .044, and P(M ∪ C) = .524. Find the indicated probability.
17) P(M' ∪ C')
A) .466
B) .524
C) .956
D) .004
4
17)
Find the odds in favor of the indicated event.
18) Rolling a 4 with a fair die.
A) 2 to 3
B) 1 to 5
C) 1 to 6
D) 1 to 4
Use the given table to find the indicated probability.
19) People were given three choices of soft drinks and asked to choose one favorite. The following
table shows the results.
under 21 years of age
between 21 and 40
over 40 years of age
19)
cola root beer lemon-lime
40
25
20
35
20
20
30
P(person drinks root beer person is over 40)?
2
A)
5
C)
18)
30
35
B)
6
17
2
17
D) None of the above
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.
Find the probability of the indicated result.
20) One marble is white, and one marble is blue.
20)
1
1
3
3
A)
B)
C)
D)
4
2
28
56
Solve the problem.
21) If two fair dice are rolled, find the probability that the roll is a double given that the sum is 11.
1
1
1
A) 0
B)
C)
D)
3
4
2
5
21)
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.
Find the probability of the indicated result.
22) One marble is green, and one marble is red.
22)
1
1
1
3
A)
B)
C)
D)
4
2
7
28
Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the
probability.
23) Three balls are drawn from a bag containing 5 red and 3 green balls. The number of green balls is
23)
counted.
A)
B)
C)
D)
x P
x P
x P
x P
0 1/3
0 1/6
0 .179
0 .018
1 1/6
1 1/3
1 .536
1 .268
2 1/6
2 1/3
2 .268
2 .536
3 1/3
3 1/6
3 .018
3 .179
Find the expected value for the random variable.
24) A business bureau gets complaints as shown in the following table. Find the expected number of
complaints per day.
Complaints per Day
Probability
A) 2.98
0 1 2 3 4 5
.04 .11 .26 .33 .19 .07
B) 3.01
C) 2.85
D) 2.73
Solve the problem.
25) A contractor is considering a sale that promises a profit of $26,000 with a probability of .7 or a loss
(due to bad weather, strikes, and such) of $18,000 with a probability of .3. What is the expected
profit?
A) $8000
B) $18,200
C) $30,800
D) $12,800
6
24)
25)
Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the
probability.
26) A field goal kicker has a kicking average of .75 and he tries 3 field goals in a game. The number of
26)
field goals is counted.
A)
B)
C)
D)
x P
x P
x P
x P
0 .422
0 .016
0 .016
0 .522
1 .141
1 .141
1 .140
1 .141
2 .016
2 .422
2 .522
2 .322
3 .422
3 .422
3 .322
3 .016
Find the expected value for the random variable.
27)
z
24
26
28
30
32
P(z) 0.14 0.12 0.46 0.26 0.08
A) 22.26
B) 29.72
C) 29.00
D) 28
Solve the problem.
28) In a game of musical chairs, 11 children will sit in 10 chairs arranged in a row (one child will not
find a chair). In how many ways can 10 of the children find seats?
A) 39,916,800
B) 3,628,800
C) 39,916,940
D) 110
Use the multiplication principle to solve the problem.
29) If 6 newborn babies are randomly selected, how many different gender sequences are possible?
A) 12
B) 64
C) 720
D) 36
30) How many different 4-letter radio station call letters can be made if repeats are allowed and the
first letter must be K.
A) 456,976
B) 78
C) 17,576
D) 1000
7
27)
28)
29)
30)
Solve the problem.
31) If the police have 8 suspects, how many different ways can they select 5 for a lineup?
A) 40 ways
B) 56 ways
C) 336 ways
D) 6720 ways
Evaluate the expression.
32) 6 P4
A) 1
B) 21
C) 0
D) 720
Solve the problem.
33) An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the
same floor considering that it is equally likely that a person will get off at any floor.
A) .410
B) .500
C) .910
D) .610
31)
32)
33)
A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the
probability.
34) 1 cherry, 2 lemon
34)
A) .0303
B) .0424
C) .0364
D) .3636
35) 2 orange, 1 lemon
A) .3636
B) .0303
C) .0364
D) .1091
35)
Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand
is made up of 13 cards.
36) In bridge, 6 of one suit, 4 of another, and 3 of another
36)
A) .0060
B) .00055
C) .0022
D) .0133
8
37) In bridge, all cards in one suit
A) 3.14 × 10-11
B) 3.14 × 10-12
C) 6.30 × 10-12
D) 1.57 × 10-12
37)
A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result.
38) Exactly one four
38)
A) .003
B) .402
C) .502
D) .116
Find the requested probability.
39) A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly two fours?
A) .5681
B) .0621
C) .7182
D) .2009
39)
In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability of the event from a
random sample of 10 students who are physics majors.
40) Exactly 4 do not belong to an ethnic minority.
40)
A) .0467
B) .0547
C) .2253
D) .2564
Find the requested probability.
41) A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four fives?
A) .5360
B) .3125
C) .0080
D) .9688
42) What is the probability that 14 rolls of a fair die will show three ones?
A) .0454
B) .4536
C) .1134
9
D) .2268
41)
42)
Answer Key
Testname: 1324_HCC_TEST 3_8-9_REVIEW
1) C
2) C
3) A
4) B
5) C
6) D
7) A
8) D
9) A
10) C
11) D
12) B
13) A
14) C
15) B
16) D
17) C
18) B
19) C
20) C
21) A
22) C
23) C
24) D
25) D
26) B
27) B
28) A
29) B
30) C
31) B
32) D
33) A
34) C
35) C
36) D
37) C
38) B
39) D
40) B
41) C
42) D
10