Math 1342 Ch, 4-6 Review Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
What is the set of all possible outcomes of a probability experiment?
A) events
B) a Venn diagram
C) an outcome
D) the sample space
1)
2)
What type of probability uses a knowledge of sample spaces as opposed to experiments
to determine the numerical probability that an event will occur?
A) classical probability
B) empirical probability
C) conditional probability
D) subjective probability
2)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
3)
If two dice are rolled one time, find the probability of getting a sum less than 5.
3)
4)
A section of an exam contains two multiple-choice questions, each with three
answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally
likely, find the probability (as a reduced fraction) that both answers are the same
("AA", "BB" or "CC"). [Hint: List all the outcomes of the sample space first.]
4)
5)
The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers,
2 executives, and 50 factory workers. If a person is selected at random, what is
the probability that he or she is a factory worker?
5)
6)
A survey asked 32,011 homeowners how many pets they owned. The results were 6)
as followed:
Number of Pets
0
1
2
3
4 or more
Total
Number of Homeowners
5583
10,423
8856
6349
800
32,011
What is the probability that a sampled homeowner has three pets?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
7)
A jar contains four white marbles, five red marbles, and six black marbles. If a marble
2
were selected at random, the probability that it is white or black would be .
3
A) True
B) False
1
7)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
8)
A single card is drawn from a deck. Find the probability of selecting a heart or a
8.
8)
9)
An apartment building has the following distribution of apartments:
1 bedroom
2 bedroom
3 bedroom
1st floor 3
1
1
2nd floor 0
4
2
3rd floor 1
4
1
If an apartment is selected at random, what is the probability that it is not a 2
bedroom apartment on the 2nd floor?
9)
10) If
one card is drawn from an ordinary deck of cards, what is the probability that
the card will be an ace, a king of hearts, or a spade?
10)
11) In
11)
a recent semester at a local university, 500 students enrolled in both General
Chemistry and Calculus I. Of these students, 66 received an A in general
chemistry, 73 received an A in calculus, and 33 received an A in both general
chemistry and calculus.
Find the probability that a randomly chosen student received an A in general
chemistry or calculus or both.
12) A
poll was taken of 14,499 working adults aged 40-70 to determine their level of
education. The participants were classified by sex and by level of education. The
results were as follows.
Education Level
High School or Less
Bachelor's Degree
Master's Degree
Ph.D.
Total
Male
3157
3723
529
50
7459
Female
2794
3714
482
50
7040
12)
Total
5951
7437
1011
100
14,499
A person is selected at random. Compute the probability that the person is female
and has a bachelor's degree.
13) If
P(A) = 0.38, P(B) = 0.33, and P(A and B) = 0.24, find P(A or B).
P(A) = 0.35, P(B) = 0.85, and P(A or B) = 0.86, are A and B mutually
exclusive?
14) If
2
13)
14)
15) Let A
and B be events with P(A) = 0.7, P(B) = 0.3, and P(B|A) = 0.2. Find
P(A and B).
15)
16) Let A
16)
17) A
17)
18) A
18)
and B be events with P(A) = 0.5, P(B) = 0.4. Assume that A and B are
independent. Find P(A and B).
fair die is rolled four times. What is the probability that it comes up 1 at least
once?
lot of 1000 components contains 150 that are defective. Two components are
drawn at random and tested. Let A be the event that the first component drawn is
defective, and let B be the event that the second component drawn is defective.
Find P(A).
19) According
to popular belief, 80% of adults enjoy drinking beer. Choose a group
of 4 adults at random. The probability that all of them enjoy drinking beer is:
19)
20) In
20)
21) Urn
21)
22) It
22)
23) There
23)
24) A
24)
a second grade class containing 12 girls and 11 boys, 2 students are selected at
random to give out the math papers. What is the probability that both are girls?
1 contains 3 red balls and 4 black balls. Urn 2 contains 4 red balls and 2
black balls. Urn 3 contains 6 red balls and 5 black balls. If an urn is selected at
random and a ball is drawn, find the probability it will be red.
has been reported that 3% of all cars on the highway are traveling at speeds in
excess of 70 mph. If the speeds of four random automobiles are measured via
radar, what is the probability that at least one car is going over 70 mph?
are 3 blue balls, 5 red balls, and 2 white balls in a bag of balls. If a person
selects two of the balls, what is the probability that the second one is blue given
that the first one was white?
box contains blue chips and red chips. A person selects two chips without
1
replacement. If the probability of selecting a blue chip and a red chip is , and
4
the probability of selecting a blue chip on the first draw is
5
, find the
16
probability of selecting the red chip on the second draw, given that the first chip
selected was a blue chip.
25) A
store manager wants to display 4 different brands of toothpaste in a row. How
many ways can this be done?
3
25)
26) There
are 3 different mathematics courses, 3 different science courses, and 5
different history courses. If a student must take one of each, how many different
ways can this be done?
26)
27) How
27)
28) Three statistics
28)
29) If
29)
30) If
30)
31) A
31)
many different ways can four people: Andy, Betty, Cindy, and Doug, sit in
a row at the opera if Andy and Betty must sit together?
professors and seven chemistry professors are available to be
advisors to a student organization. The student organization needs two of the
professors to be advisors. If each professor has an equal chance of being
selected, what is the probability that both professors are chemistry professors?
20 tickets are sold and 2 prizes are to be awarded, find the probability that one
person will win both prizes if that person buys exactly 2 tickets.
five cards are drawn from a deck of cards without replacement, what is the
probability that at least one of the cards is a heart?
committee consist of 8 women and 11 men. Three members are chosen as
officers. What is the probability that all three officers are women?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
32) The
sum of the probabilities of all the events in the sample space of a probability
distribution must equal 1.
A) True
B) False
32)
33) The
33)
34) Which
34)
following distribution is not a probability distribution because
-2
-1
0
1
2
X
0.16
0.15
0.42
0.13
0.31
P(X)
A) the probability values are not increasing.
B) the probability values are not discrete.
C) the values of the variable are negative.
D) the probability values do not add to 1.
of the following variables are continuous?
i. an automobile's gas mileage
ii. the air pressure in an automobile's spare tire
iii. an automobile's sticker price
A) i and ii
B) i, ii, and iii
C) i
D) None are continuous.
4
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
35) The
35)
following table presents the probability distribution of the number of
vacations X taken last year for a randomly chosen family. Find the probability that
a family took at least 3 vacations last year.
x
0
P(x) 0.05
36) What
2
0.17
3
0.07
4
0.02
is the standard deviation of the following probability distribution?
36)
0
2
4
6
8
0.20 0.05 0.35 0.25 0.15
X
P(X)
37) Give
1
0.69
the mean of the following probability distribution.
37)
2
3
4
5
0.50 0.25 0.15 0.10
X
P(X)
38) The
following table presents the probability distribution of the number of
vacations X taken last year for a randomly chosen family. Compute the standard
deviation σ.
x
0
P(x) 0.06
1
0.67
2
0.18
3
0.07
38)
4
0.02
39) Compute
the standard deviation of the random variable with the given discrete
probability distribution.
39)
x
P(x)
0 0.2
5 0.45
15 0.05
25 0.3
40) If
a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a
sum of three, he wins $20. The cost to play the game is $5. What is the
expectation of this game?
5
40)
the probability of X successes.
n = 5, X = 4, p = 0.7
41) Compute
41)
42) Determine
42)
43) It
43)
44) A
student takes a 18-question, multiple-choice exam with four choices for each
question and guesses on each question. Find the probability of guessing exactly 7
out of 18 correctly.
44)
45) Find
the variance for the values of n and p when the conditions for the binomial
distribution are met.
n = 500, p = 0.75
45)
46) A
46)
47) A
47)
48) Use
48)
49) If
49)
the indicated probability for a binomial experiment with the given
number of trials n and the given success probability p.
n =12, p = 0.7, P(3 or fewer)
is estimated that 25% of households own a riding lawn mower. A sample of 16
households is studied. What is the probability that exactly 5 of these own a riding
lawn mower?
university has 10,000 students of which 35% are male and 65% are female. If
a class of 30 students is chosen at random from the university population, find
the mean and variance of the number of male students.
computer store has 75 printers of which 25 are laser printers and 50 are ink jet
printers. If a group of 10 printers is chosen at random from the store, find the
mean and variance of the number of ink jet printers.
the multinomial formula and find the probability for the following data.
n =6, X1 = 3, X2 = 2, X3 = 1,
p1 = 0.58, p2 = 0.25, p3 = 0.17
there are 20 typographical errors randomly distributed in a 250-page document,
find the probability that a given page contains exactly two errors.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
50) In
the instructor's answer book for a mathematics text, 8% of the answers are incorrect.
Use the Poisson approximation to express the probability that there are exactly 2
incorrect answers for a homework set with 50 problems.
e-8 82
e-424
e-4 42
e-828
A)
2!
B)
C)
4!
6
2!
D)
8!
50)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
51) In
a batch of 100 cell phones, there are, on average, 6 defective ones. If a random
sample of 25 is selected, find the probability of 3 defective ones.
51)
52) The
52)
53) For
53)
number of typographical errors in a document follows a Poisson distribution
with a mean of 4 errors per page. Let X represent the number of errors on 2
pages. Find P(Greater than 1).
a normal distribution curve with a mean of 15 and a standard deviation of 5,
which range of the variable defines an area under the curve corresponding to a
probability of approximately 68%?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
54) Which
of the following properties distinguishes the standard normal distribution from
other normal distributions?
A) The curve is continuous.
B) The mean is located at the center of the distribution.
C) The mean is 0 and the standard deviation is 1.
D) The total area under the curve is equal to 1.00.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
55) Find
the area under the standard normal distribution curve between z = 0 and z =
2.16.
7
55)
54)
is the area under the standard normal distribution curve between z = 1.50
and z = 2.50?
56) What
56)
57) Find
the probability P(0 < z < 1.67), using the standard normal distribution.
57)
58) Find
the z value that corresponds to the given area.
58)
59) If
a normally distributed group of test scores have a mean of 70 and a standard
deviation of 12, find the percentage of scores that will fall below 50.
59)
60) The
60)
average length of crocodiles in a swamp is 11.5 feet. If the lengths are
normally distributed with a standard deviation of 1.7 feet, find the probability
that a crocodile is more than 11 feet long.
8
61) X
61)
62) X
62)
63) For
63)
64) A
64)
65) A
65)
66) Use
66)
is a normally distributed random variable with a mean of 11.00. If the
probability that X is less than 11.88 is 0.67 (as shown below), then what is the
standard deviation of X? (Note: the diagram is not necessarily to scale.)
is a normally distributed random variable with a standard deviation of 2.00.
Find the mean of X if 12.71% of the area under the distribution curve lies to the
right of 10.28. (Note: the diagram is not necessarily to scale.)
a normal distribution with a mean of 13 and a standard deviation of 6, the
value 1 has a z value of
sample of size 52 will be drawn from a population with mean 18 and standard
deviation 13. Find the probability that x will be less than 21.
ferry will safely accommodate 91 tons of passenger cars. Assume that the
mean weight of a passenger car is 2.1 tons with standard deviation 0.7 tons. If a
random sample of 40 cars are loaded onto the ferry, what is the probability that
the maximum safe weight will be exceeded?
the normal approximation to the binomial to find that probability for the
specific value of X.
n = 30, p = 0.4, X = 5
9
67) Use
the normal approximation to find the indicated probability. The sample size
is n, the population proportion of successes is p, and X is the number of successes
in the sample.
n = 78, p = 0.59: P(X > 42)
67)
68) A
68)
69) A
69)
70) A
70)
gardener buys a package of seeds. Seventy-six percent of seeds of this type
germinate. The gardener plants 110 seeds. Approximate the probability that
fewer than 77 seeds germinate.
biologist estimates that 70% of the deer in a region carry a certain type of tick.
For a sample of 300 deer selected at random, what is the chance that 216 or
fewer deer have this tick?
magazine reported that 6% of American drivers admit to reading the
newspaper while driving. If 500 drivers are selected at random, find the
probability that exactly 40 will admit to reading the newspaper while driving.
10
Answer Key
Testname: MATH1342 CH. 4,5,6 REVIEW
1) D
2) A
3)
1
6
1/3
5
5)
8
4)
6) 0.198
7) A
8)
4
13
9)
13
17
10)
17
52
11) 0.212
12) 0.256
13) 0.47
14) No
15) 0.14
16) 0.2
17) 0.5177
18) 0.15
19) 0.410
20)
12 1
∙
23 2
21)
379
693
22) 0.11
23)
1
3
24)
4
5
25) 24
26) 45
27) 12
28) 0.467
11
Answer Key
Testname: MATH1342 CH. 4,5,6 REVIEW
29)
1
190
30) 0.778
31) 0.0578
32) A
33) D
34) A
35) 0.09
36) 2.6
37) 2.85
38) 0.77
39) 10.0
40) –$3.06
41) 0.360
42) 0.0017
43) 0.1802
44) 0.082
45) 93.75
46) Mean
= 10.5, Variance = 6.8
47) Mean = 6.7, Variance = 2.2
48) 0.124
49) 0.0030
50) C
51) 0.1303
52) 0.9970
53) from 10
54) C
55) 0.4846
to 20
56) 0.0606
57) 45.25%
58) –0.22
59) 4.75%
60) 0.62
61) 2.00
62) 8.0
63) -2
64) 0.9515
65) 0.0571
66) 0.20
67) 0.7910
68) 0.0559
12
Answer Key
Testname: MATH1342 CH. 4,5,6 REVIEW
69) 0.794
70) 1.3%
13