Download MGF 1106 Summer C 12 Ref

MGF 1106 Summer C 12 Ref: 687619
Review for Exam 4
Mr. Guillen
Exam 4 will be on 07/19/12 and cover the following sections: 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
1) Suppose there are 4 roads connecting town A to town B and 3 roads connecting town B to
town C. In how many ways can a person travel from A to C via B?
1)
2) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if
repetitions of digits are allowed?
2)
3) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions
are not allowed?
3)
4) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions
are not allowed?
4)
5) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if
repetitions of digits are allowed?
5)
6) How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions
are not allowed?
6)
7) License plates are made using 2 letters followed by 2 digits. How many plates can be
made if repetition of letters and digits is allowed?
7)
8) License plates are made using 2 letters followed by 2 digits. How many plates can be
made if repetition of letters and digits is allowed?
8)
9) At a lumber company that sold shelves, a customer could choose from 4 types of wood, 4
different widths and 5 different lengths. How many different types of shelves could be
ordered?
9)
10) How many different three-digit numbers can be written using digits from the set {2, 3, 4,
5, 6} without any repeating digits?
10)
11) A license plate is to consist of 2 letters followed by 5 digits. Determine the number of
different license plates possible if repetition of letters and numbers is not permitted.
11)
12) A license plate is to consist of 2 letters followed by 4 digits. Determine the number of
different license plates possible if repetition of letters and numbers is not permitted.
12)
13) A license plate is to consist of 3 letters followed by 4 digits. Determine the number of
different license plates possible if the first letter must be an N , M , or P and repetition of
letters and numbers is not permitted.
13)
14) A license plate is to consist of 3 letters followed by 5 digits. Determine the number of
different license plates possible if the first letter must be an N , M , or P and repetition of
letters and numbers is not permitted.
14)
Evaluate the expression.
15) 10P4
15)
16) 6P0
16)
17) 12P8
17)
18) 11P3
18)
19) 9P5
19)
20) 14P5
20)
An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul.
21) In how many ways can the people be presented?
21)
Suppose a traveler wanted to visit a museum, an art gallery, and the state capitol building. 45-minute tours are offered
at each attraction hourly from 10 a.m. through 3 p.m. (6 different hours). Solve the problem, disregarding travel time.
22) In how many ways can the traveler visit all three places in one day?
22)
23) In how many ways could the traveler schedule two of the three tours in one day?
23)
24) In how many ways could the traveler schedule all three tours before 1 p.m.?
24)
Solve the problem.
25) How many different three-number "combinations" are possible on a combination lock
having 23 numbers on its dial? Assume that no numbers repeat. (Combination locks are
really permutation locks.)
25)
26) There are 9 horses in a race. In how many ways can the first three positions of the order of
the finish occur? (Assume there are no ties.)
26)
27) How many ways can the letters in the word "WISCONSIN" be arranged?
27)
How many distinguishable permutations of letters are possible in the word?
28) CRITICS
28)
29) LOOK
29)
30) GIGGLE
30)
31) TENNESSEE
31)
32) MISSISSIPPI
32)
33) COMMITTEE
33)
Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, count the different ways of
choosing the following officers or representatives for student congress. Assume that no one can hold more than one
office.
34) Four representatives
34)
35) Three representatives, if two must be female and one must be male
35)
36) A president, a secretary, and a treasurer, if the president must be a woman and the other
two must be men
36)
Four accounting majors, two economics majors, and three marketing majors have interviewed for five different
positions with a large company. Find the number of different ways that five of these could be hired.
37) Two accounting majors must be hired first, then one economics major, then two marketing 37)
majors.
Evaluate the expression.
38) 8C5
38)
39) 11C8
39)
40) 9C6
40)
41) 12C7
41)
42) 6C1
42)
43) 10C1
43)
44) 12C7
44)
Solve the problem.
45) How many ways can a committee of 2 be selected from a club with 12 members?
45)
46) In how many ways can a student work 6 out of 10 questions on an exam?
46)
47) How many ways can a committee of 4 be selected from a club with 10 members?
47)
48) If the police have 7 suspects, how many different ways can they select 5 for a lineup?
48)
49) In how many ways can a group of 9 students be selected from 10 students?
49)
50) A bag contains 7 apples and 5 oranges. If you select 6 pieces of fruit without looking, how
many ways can you get 6 apples?
50)
51) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how
many ways can you get 4 oranges?
51)
52) How many 5-card poker hands consisting of 3 aces and 2 kings are possible with an
ordinary 52-card deck?
52)
53) Bob is planning to pack 6 shirts and 4 pairs of pants for a trip. If he has 11 shirts and 7
pairs of pants to choose from, in how many different ways can this be done?
53)
Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain the
following cards?
54) All four kings
54)
55) All red cards
55)
56) No face cards
56)
57) All spades
57)
Find the number of ways to get the following card combination from a 52-card deck.
58) Two red cards and three black cards
58)
59) No face cards in a five-card hand
59)
60) Two black queens and two red jacks
60)
61) One spade, two diamonds, and two hearts
61)
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.
62) All cherry
62)
63) 2 cherry, 1 lemon
63)
64) All lemon
64)
65) One of each flavor
65)
66) 2 orange, 1 lemon
66)
67) 1 cherry, 2 lemon
67)
Solve.
68) A 6-sided die is rolled. What is the probability of rolling a number less than 6?
68)
69) Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the
die will be 3?
69)
70) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on
the dice will be greater than 9?
70)
Find the probability of the given event.
71) A single fair die is rolled. The number on the die is a 3 or a 5.
71)
72) A single fair die is rolled. The number on the die is greater than 2.
72)
73) A single fair die is rolled. The number on the die is not 6.
73)
74) A single fair die is rolled. The number on the die is a multiple of 3.
74)
75) A single fair die is rolled. The number on the die is prime.
75)
76) Two fair dice are rolled. The sum of the numbers on the dice is 5.
76)
77) Two fair dice are rolled. The sum of the numbers on the dice is 6 or 10.
77)
78) Two fair dice are rolled. The sum of the numbers on the dice is greater than 10.
78)
Find the probability.
79) When a single card is drawn from a well-shuffled 52-card deck, find the probability of
getting a king.
79)
80) When a single card is drawn from a well-shuffled 52-card deck, find the probability of
getting a black 7.
80)
81) When a single card is drawn from a well-shuffled 52-card deck, find the probability of
getting a club.
81)
82) When a single card is drawn from a well-shuffled 52-card deck, find the probability of
getting the 4 of hearts.
82)
83) When a single card is drawn from a well-shuffled 52-card deck, find the probability of
getting a black 5 or a black 4.
83)
84) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing
an ace or a 7?
84)
85) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing
a face card or a 6?
85)
86) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing
a heart, club, or diamond?
86)
87) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing
a black card that is not a face card?
87)
88) A bag contains 4 red marbles, 7 blue marbles, and 2 green marbles. What is the
probability that a randomly selected marble is blue?
88)
89) A lottery game has balls numbered 1 through 15. What is the probability that a randomly
selected ball is an even numbered ball or a 12?
89)
90) A bag contains 7 red marbles, 2 blue marbles, and 1 green marble. What is the probability
that a randomly selected marble is not blue?
90)
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.
91) In bridge, exactly 3 kings and exactly 3 queens
91)
92) In bridge, 4 aces
92)
93) In bridge, all cards in one suit
93)
Find the odds.
94)
94)
What are the odds of drawing a 3 from these cards?
95)
95)
What are the odds of drawing an even number from these cards?
96)
96)
What are the odds of drawing a number greater than 2 from these cards?
97) A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds for
the cube showing an odd number?
97)
98) A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds for
the cube showing a 4?
98)
99) A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds for
the cube showing a number less than 3?
99)
100) The kings are separated from a deck of standard playing cards and shuffled. One is
randomly selected. What are the odds in favor of drawing a black card?
100)
101) Seven slips of paper marked with the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in a box and
mixed well. Two are drawn. What are the odds that the sum of the numbers on the two
selected slips is not 5?
Solve the problem.
102) The odds in favor of a horse winning a race are posted as 9 : 2. Find the probability that
the horse will win the race.
101)
102)
103) The odds in favor of a horse winning a race are posted as 7 : 5. Find the probability that
the horse will lose the race.
103)
104) The odds in favor of Carl beating his friend in a round of golf are 7 : 4 Find the
probability that Carl will beat his friend.
104)
105) The odds in favor of Carl beating his friend in a round of golf are 3 : 2. Find the
probability that Carl will lose.
105)
106) The odds against Carl beating his friend in a round of golf are 4 : 3. Find the probability
that Carl will beat his friend.
106)
107) The odds against Carl beating his friend in a round of golf are 9 : 7. Find the probability
that Carl will lose.
107)
108) The odds in favor of Jerome beating his friend in a round of golf are 1 : 5. Find the
probability that Jerome will beat his friend.
108)
109) The odds in favor of Trudy beating her friend in a round of golf are 1 : 8. Find the
probability that Trudy will lose.
109)
110) The odds against Chip beating his friend in a round of golf are 1 : 9. Find the probability
that Chip will beat his friend.
110)
111) The odds against Muffy beating her friend in a round of golf are 1 : 4. Find the probability
that Muffy will lose.
111)
112) If two cards are drawn without replacement from a deck, find the probability that the
second card is a spade, given that the first card was a spade.
112)
113) If two cards are drawn without replacement from a deck, find the probability that the
second card is red, given that the first card was a heart.
113)
114) If two cards are drawn without replacement from a deck, find the probability that the
second card is a face card, given that the first card was a queen.
114)
115) If two cards are drawn without replacement from a deck, find the probability that the
second card is an ace, given that the first card was an ace.
115)
116) If three cards are drawn without replacement from a deck, find the probability that the
third card is a heart, given that the first two cards were hearts.
116)
117) If three cards are drawn without replacement from a deck, find the probability that the
third card is a face card, given that the first card was a queen and the second card was a 5.
117)
Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the
probability.
118) The second marble is red given the first marble is white.
118)
119) The second marble is white given the first marble is blue.
119)
120) The second marble is blue given the first marble is white.
120)
121) The second marble is blue given the first marble is red.
121)
122) The second marble is blue given the first marble is blue.
122)
Answer Key
Testname: MGF_1106_SUMMER_C_EXAM_4_REVIEW
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
51)
12 ways
10,000 four-digit numbers
210 three-digit numbers
210 three-digit numbers
10,000 four-digit numbers
2520 five-digit numbers
67,600 plates
67,600 plates
80 types
60 three-digit numbers
19,656,000
3,276,000
9,072,000
54,432,000
5040
1
19,958,400
990
15,120
240,240
5,040
120
30
6
10,626 three-number "combinations"
504
45,360
1260
12
120
3780
34,650
45,360
120
6
12
144 ways
56
165
84
792
6
10
792
66 ways
210 ways
210 ways
21 ways
10 ways
7 ways
0 ways
Answer Key
Testname: MGF_1106_SUMMER_C_EXAM_4_REVIEW
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
24 five-card hands
16,170
48 hands
65,780 hands
658,008 hands
1287 hands
845,000 ways
658,008 ways
48 ways
79,092 ways
.1212
.1818
0
.2182
.0364
.0364
5
68)
6
69)
1
18
70)
1
6
71)
1
3
72)
2
3
73)
5
6
74)
1
3
75)
1
2
76)
1
9
77)
2
9
78)
1
12
79)
1
13
80)
1
26
81)
1
4
82)
1
52
Answer Key
Testname: MGF_1106_SUMMER_C_EXAM_4_REVIEW
83)
1
13
84)
2
13
85)
4
13
86)
3
4
87)
5
13
88)
7
13
89)
7
15
90)
4
5
91) .00097
92) .00264
6.30 x 10-12
1:4
2:3
3:2
1:1
1:5
1:2
1 to 1
19 to 2
9
102)
11
93)
94)
95)
96)
97)
98)
99)
100)
101)
103)
5
12
104)
7
11
105)
2
5
106)
3
7
107)
9
16
108)
1
6
109)
8
9
110)
9
10
Answer Key
Testname: MGF_1106_SUMMER_C_EXAM_4_REVIEW
111)
1
5
112)
4
17
113)
25
51
114)
11
51
115)
1
17
116)
11
50
117)
11
50
118)
2
7
119)
3
7
120)
1
7
121)
1
7
122) 0
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