Download Review for Test 5 over chapter 7 SHORT ANSWER. Write the word

Review for Test 5 over chapter 7
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
5) A card is drawn from a well-shuffled deck of
52 cards. What is the probability of drawing a
face card or a 4?
Find the indicated probability.
1) 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
that the first marble is white and the second
marble is blue.
6) The distribution of B.A. degrees conferred by a
local college is listed below, by major.
Major
English
Mathematics
Chemistry
Physics
Liberal Arts
Business
Engineering
2) The following contingency table shows the
popular votes cast in the 1984 presidential
election by region and political party. Round
your answer to three decimal places.
Political Party
Region
Democratic Republican Other
Northeast
9046
11,336
101
Midwest
10,511
14,761
169
South
10,998
17,699
136
West
7022
10,659
214
Totals
37,577
54,455
620
What is the probability that a randomly
selected degree is in Engineering?
A die is rolled twice. Write the indicated event in set
notation.
7) The first roll is a 2.
A person who voted Democratic in the 1984
presidential election is selected at random.
Find the probability that the person was from
the West.
Solve the problem.
8) If three cards are drawn without replacement
from an ordinary 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.
3) When two balanced dice are rolled, there are
36 possible outcomes. Find the probability that
either doubles are rolled or the sum of the dice
is 10.
9) A survey revealed that 30% of people are
entertained by reading books, 38% are
entertained by watching TV, and 32% are
entertained by both books and TV. What is the
probability that a person will be entertained by
either books or TV? Express the answer as a
percentage.
4) The following contingency table provides a
joint frequency distribution for a group of
retired people by career and age at retirement.
Age at
Retirement
50-55
Attorney
8
College Professor
8
Administrative Assistant 21
Store Clerk
18
Total
55
56-60
47
50
45
44
186
Frequency
2073
2164
318
856
1358
1676
868
9313
10) The odds in favor of Trudy beating her friend
in a round of golf are 1 : 5. Find the
probability that Trudy will lose.
61-65
77
86
63
70
296
11) Bill has 6 friends over for dinner. After dinner,
the seven of them are thinking about going out
dancing. Not everyone is sure that they want
to go. How many subsets of the seven are
possible if at least two people go dancing?
Suppose one of these people is selected at
random. Compute the probability that the
person selected was a store clerk.
1
Write the sample space for the given experiment.
17) For the purposes of a public opinion poll,
respondents are classified as male or female
and as high income, middle income, or low
income.
12) The manager of a bank recorded the amount of
time each customer spent waiting in line
during peak business hours one Monday. The
table below summarizes the results.
Waiting Time Number of
(minutes) Customers
0-3
13
4-7
14
8-11
12
12-15
5
16-19
4
20-23
3
24-27
1
Use a Venn diagram to find the indicated probability.
18) If P(A ∩ B) = 0.18, P(A) = 0.31, and P(B) = 0.48,
find P(A ∪ B).
Provide an appropriate response.
19) A card is drawn at random from a
well-shuffled deck of 52 cards.
Let A be the event that the card is a heart.
Let B be the event that the card is a king.
Find P(A), P(B), and P(A ∩ B). Are events A
and B independent? How can you tell?
If we randomly select one of the times
represented in the table, what is the probability
that it is at least 12 minutes or between 8 and
15 minutes? Round to the nearest thousandth
when necessary.
20) Assume that the events A1 , A2 , . . . , An are
mutually exclusive events whose union is the
sample space, and that B is an event that has
occurred. Use Bayes' theorem to write an
equation for P(A1 ∣B).
13) In a certain U.S. city, 51.8% of adults are
women. In that city, 14% of women and 10% of
men suffer from depression. If an adult is
selected at random from the city, find the
probability that the person suffers from
depression.
21) Two cards are selected at random from a
standard deck of 52 cards. Let
A = event the first card is a queen
B = event the second card is a queen.
Use a Venn diagram to decide if the statement is true or
false.
14) A' ∪ (B ∩ C) = (A' ∪ B) ∩ (A' ∪ C)
(a) If the first card is replaced before the second
one is drawn, are events A and B independent?
Which rule could you use to find P(A & B)?
(b) If the first card is not replaced before the
second one is drawn, are events A and B
independent? Which rule could you use to find
P(A & B)?
22) Assume that E and F are events. Must the
union of E and F also be an event? Must the
intersection of E and F also be an event?
Let U = {all soda pops}; A = {all diet soda pops};
B = {all cola soda pops}; C = {all soda pops in cans}; and
D = {all caffeine-free soda pops}. Describe the given set in
words.
15) C' ∪ D'
Find the probability of the given event.
16) Two fair dice are rolled. The sum of the
numbers on the dice is greater than 9.
2
30) A' ∪ B'
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. If the assignment is not
possible, tell why.
23)
Outcomes Probabilities
a
5/16
b
5/8
c
1/8
d
-1/16
Decide whether the statement is true or false.
31) {8, 13, 6} ∪ ∅ = {8, 13, 6}
Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and
U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given
statement is true or false.
24) U ⊆ A
Find the number of elements in the indicated set by
referring to the given table.
32) V ∩ W,
given the following table:
U.S. Production (in Thousands of Tons) of Certain Nu
Year
Pecans (P) Almonds (A) Walnuts (W)
1993 (T)
184
584
232
1994 (F)
99
587
232
1995 (V)
134
304
231
1996 (S)
111
412
205
Find the number of subsets of the set.
25) {1, 2, 3, . . . , 7}
Use a Venn Diagram and the given information to
determine the number of elements in the indicated region.
26) 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)
The table shows, for some particular year, a listing of
several income levels and, for each level, the proportion of
the population in the level and the probability that a
person in that level bought a new car during the year.
Given that one of the people who bought a new car during
that year is randomly selected, find the probability that
that person was in the indicated income category. Round
your answer to the nearest hundredth.
Solve the problem using Bayes' Theorem. Round the
answer to the nearest hundredth, if necessary.
27) For mutually exclusive events X1 , X2 , and X3 ,
let P(X1 ) = 0.11, P(X2 ) = 0.40, and P(X3 ) = 0.49.
Also, P(Y∣X 1 ) = 0.40, P(Y∣X2 ) = 0.30 and P(Y
∣X3 ) = 0.60. Find P(X3 ∣Y).
Income level
$0 - 4,999
$5,000 - 9,999
$10,000 - 14,999
$15,000 - 19,999
$20,000 - 24,999
$25,000 - 29,999
$30,000 - 34,999
$35,000 - 39,999
$40,000 - 49,999
$50,000 and over
Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y};
B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of
the indicated set, using set braces.
28) A ∪ (B ∩ C)
Shade the Venn diagram to represent the set.
29) (A' ∪ B) ∩ C
Proportion
Probability that
of population bought a new car
5.2%
0.02
6.4%
0.03
5.4%
0.06
8.7%
0.07
9.4%
0.09
10.2%
0.10
13.8%
0.11
10.7%
0.13
15.5%
0.15
14.7%
0.19
33) $35,000 - $39,999
3
Use the given table to find the indicated probability.
34) The following table contains data from a study
of two airlines which fly to Smalltown, USA.
Number of flights
arrived on time
Podunk Airlines
33
Upstate Airlines
43
Find the probability.
38) A family has five children. The probability of
having a girl is 1/2. What is the probability of
having 2 girls followed by 3 boys? Round your
Number of flights
answer to four decimal places.
arrived late
6
39) A bag contains 19 balls numbered 1 through
5
19. What is the probability that a randomly
selected ball has an even number?
If a flight is selected at random, what is the
probability that it was on Upstate Airlines
given that it arrived late?
40) 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?
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)
41) Assuming that boy and girl babies are equally
likely, find the probability that a family with
three children has all boys given that the first
two are boys.
Louisiana
soybeans (s)
sugarcane (n)
rice (r)
corn (c)
cotton (t)
Use Bayes' rule to find the indicated probability.
42) The incidence of a certain disease in the town
of Springwell is 3%. A new test has been
developed to diagnose the disease. Using this
test, 94% of those who have the disease test
positive while 6% of those who do not have the
disease test positive ("false positive"). If a
person tests positive, what is the probability
that he or she actually has the disease?
Let U be the smallest possible 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.
35) A ∩ K
Use the rule of total probability to find the indicated
probability.
43) Two stores sell a certain product. Store A has
30% of the sales, 2% of which are of defective
items, and store B has 70% of the sales, 5% of
which are of defective items. The difference in
defective rates is due to different levels of
pre-sale checking of the product. A person
receives one of this product as a gift. What is
the probability it is defective?
Use a Venn diagram to answer the question.
36) At East Zone University (EZU) there are 625
students taking College Algebra or Calculus.
412 are taking College Algebra, 262 are taking
Calculus, and 49 are taking both College
Algebra and Calculus. How many are taking
Calculus but not Algebra?
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.
37) Suppose a hybrid mates with a pure dominant.
If they produce two offspring, what is the
probability that neither is a hybrid?
Insert "⊆" or "⊈" in the blank to make the statement true.
44) ∅ ∅
Find the odds.
45) Find the odds in favor of drawing a red marble
when a marble is selected at random from a
bag containing 2 yellow, 5 red, and 6 green
marbles.
4
Write the indicated event in set notation.
46) The event that Charlie is selected as a board
member when three board members are
selected at random from the following group:
Allison, Betty, Charlie, Dave, and Emily.
[The possible outcomes can be represented as
follows.
ABC
ADE
ABD
BCD
ABE
BCE
ACD
BDE
ACE
CDE]
Let A = { 6, 4, 1, {3, 0, 8}, {9} }. Determine whether the
statement is true or false.
47) 4 ∈ A
Identify the probability statement as empirical or not.
48) The probability of the NFC football team
winning the Super Bowl in a randomly chosen
year is 0.55.
Use the union rule to answer the question.
49) If n(A) = 5, n(B) = 11, and n(A ∩ B) = 3; what is
n(A ∪ B)?
Determine whether the given events are mutually
exclusive.
50) Obtaining a spade and obtaining an ace when
a single card is selected from a deck of cards
Tell whether the statement is true or false.
51) {x | x is an even counting number ; 6 ≤ x ≤ 12}
= {6, 12}
5
Answer Key
Testname: UNTITLED2
1)
3
56
2) 0.187
2
3)
9
4) 0.253
4
5)
13
6) 0.0932
7) {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)}
11
8)
50
9) 36%
5
10)
6
11) 120
12) 0.481
13) 0.121
14) True
15) All soda pops that are not in cans or are caffeinated.
1
16)
6
17) {(female, high income), (female, middle income), (female, low income), (male, high income), (male, middle income),
(male, low income) }
18) 0.61
1
19) P(A) =
4
P(B) =
1
13
P(A ∩ B) =
1
52
Yes; P(A ∩ B) = P(A) · P(B)
P(A1 ) · P(B∣A1 )
20) P(A1 ∣B) =
n
∑
P(Ai) · P(B∣Ai)
i=1
21) (a) Yes, the special multiplication rule
(b) No, the general multiplication rule
22) Both the union and the intersection must be events.
23) No; a probability cannot be negative
24) False
25) 128
26) 237
27) 0.64
28) {q, s, u, w, y, z}
6
Answer Key
Testname: UNTITLED2
29)
30)
31) True
32) 231
33) 0.13
5
34)
11
35) {h, s, w}
36) 213
37) 0.25
38) 0.0313
9
39)
19
40)
5
13
41)
1
2
42) 0.326
43) 0.041
44) ⊆
45) 5 to 8
46) ABC, ACD, ACE, BCD, BCE, CDE
47) True
48) Empirical
49) 13
50) No
51) False
7