Probabliity (1) Key

AP Statistics
Final Exam Review – Probability (1)
1.
Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, then the probability
that both events occur is
a.)
b.)
c.)
d.)
e.)
2.
Ignoring twins and other multiple births, assume that babies born at a hospital are independent random
events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.
The probability that the next five babies are girls is
a.)
b.)
c.)
d.)
e.)
3.
0.125
0.333
0.667
0.750
0.875
Which of the following statements is not true?
a.)
b.)
c.)
d.)
e.)
5.
1
0.5
0.1
0.0625
0.03125
Ignoring twins and other multiple births, assume that babies born at a hospital are independent random
events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.
The probability that at least one of the next three babies is a boy is
a.)
b.)
c.)
d.)
e.)
4.
0
0.1
0.2
0.7
0.9
If two events are mutually exclusive, they are not independent.
If two events are mutually exclusive, then P(A I B) = 0.
If two events are independent, then they must be mutually exclusive.
If two events, A and B, are independent, then P(A) = P(A | B).
All four statements above are true.
In a certain town, 60% of the households have broadband interent access, 30% have at least one highdefinition television, and 20% have both. The proportion of households that have neither broadband
internet or high-definition television is:
a.)
b.)
c.)
d.)
e.)
0%
10%
30%
80%
90%
6.
Suppose that A and B are independent events with P(A) = 0.2 and P(B) = 0.4. P (A U B) is
a.)
b.)
c.)
d.)
e.)
7.
Suppose we roll two six-sided die, one red and one green. Let A be the event that the number of spots
showing on the red die is three or less and B be the event that the number of spots showing on the green
die is three or more. P(A I B) =
a.)
b.)
c.)
d.)
e.)
8.
1/3
1/4
1/8
1/9
1/12
The probability of a randomly selected adult having a rare disease for which a diagnostic test has been
developed is 0.001. The diagnostic test is not perfect. The probability that the test will be positive
(indicating that the person has the disease) is 0.99 for a person with the disease and 0.02 for a person
withouth the disease. The proportion of adults for which the test would be positive is
a.)
b.)
c.)
d.)
e.)
10.
1/6
1/4
1/3
5/6
none of these.
The card game Euchre uses a deck with 32 cards: Ace, King, Queen, Jack, 10, 9, 8, 7 of each suit.
Suppose you choose one card at random from a well-shuffled Euchre deck. What is the probability that
the card is a jack, given that you know it’s a face card?
a.)
b.)
c.)
d.)
e.)
9.
0.08
0.12
0.44
0.52
0.60
0.00002
0.00099
0.01998
0.02097
0.02100
You ask a sample of 370 people, “Should clinical trials on issues such as heart attacks that affect both
genders use subjects of just one gender?” The responses are shown in the table below. Suppose you
choose one of these people at random. What is the probability that the person said “Yes,” given that she
is a woman?
a.)
b.)
c.)
d.)
e.)
0.20
0.22
0.25
0.50
0.575
Male
Female
Yes
34
46
No
105
185
11.
Flip a coin four times. If Z = the number of heads in four flips, then the probabliity distribution of Z is
given in the table below.
Z
P(Z)
0
0.0625
1
0.2500
2
0.3750
3
0.2500
4
0.0625
The probability of at least one tail is
a.)
b.)
c.)
d.)
e.)
12.
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if
the number of spots showing is 6 you win $4, and if the number of sposts showing is 1, 2, or 3 you win
nothing. Let X be the amount that you win. Which of the following is the expected value of X?
a.)
b.)
c.)
d.)
e.)
13.
$0
$1
$2.50
$4
$6
The weight of written reports produced in a certain department has a Normal distribution with mean
60 g and standard deviation 12 g. The probability that the next report will weigh less than 45 g is
a.)
b.)
c.)
d.)
e.)
14.
0.2500
0.3125
0.6875
0.9375
none of these.
0.1056
0.3944
0.1042
0.0418
0.8944
The weights of grapefruits of a certain variety are approximately Normally distributed with a mean of 1
pound and a standard deviation of 0.12 pounds.
What is the probability that a randomly-selected grapefruit weighs more than 1.25 pounds?
a.)
b.)
c.)
d.)
e.)
0.0188
0.0156
0.3156
0.4013
0.5987
What is the probability that the total weight of three randomly selected grapefruits is more than 3.4
pounds?
a.)
b.)
c.)
d.)
e.)
nearly 0
0.0274
0.1335
0.2514
0.2611
15.
There are 20 multiple choice questions on an exam, each having responses a, b, c, or d. Each question is
worth five points and only one option per question is correct. Suppose the student guesses the answers
to each question, and the guesses from question to question are independent. Which of the following
expresses the probability that the student gets no questions correct?
a.) (0.25)20
b.) (0.75)20
 20 
c.)   (0.25)(0.75)19
1
 5
d.)   (0.25)(0.75)4
1
 5
e.)   (0.25)4(0.75)
1
16.
A worn out bottling machine does not properly apply caps to 5% of the bottles it fills. If you randomly
select 20 bottles from those produced by this machine, what is the approximate probability that exactly 2
caps have been improperly applied?
a.)
b.)
c.)
d.)
e.)
17.
0.0002
0.19
0.74
0.81
0.92
Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by
3
5
10  1   7 
a.)     
 3  8   8 
3
7
10  1   7 
b.)     
 3  8   8 
 8  1 
c.)   
 3  8 
3
7
 
8
3
7
 
8
 8  1 
d.)   
 3  8 
3
5
7
10  7   1 
e.)     
 3  8   8 
18.
7
A college basketball player makes 80% of her free throws. Suppose this probability is the same for each
free throw she attempts, and free throw attempts are independent. The probability that she makes all of
her first four free throws and then misses her fifth attempt this season is
a.)
b.)
c.)
d.)
e.)
0.32768
0.08192
0.06554
0.00128
0.00032
19.
Suppose that 40% of the cars in a certain town are white. A person stands at an intersection waiting for
a white car. Let X = the number of cars that must drive by until a white one drives by. P (X < 5) =
a.)
b.)
c.)
d.)
e.)
20.
0.0518
0.1296
0.2592
0.8704
0.9482
You flip a fair coin 5 times. The result of the first four flips is H, H, T, H. What is the probability that
the fifth flip will result in tails?
a.)
b.)
c.)
d.)
e.)
0
1/5
1/4
1/2
1
Additional questions to ponder...
1.
If the scores on the AP Statistics semester 1 final are approximately Normally distributed with a mean of
75.4 and a standard deviation of 9.2, what minimum score is needed to ensure that your score is in the
top 10% of scores on the exam?
2.
“Insert tab A into slot B” is something you might read in the assembly instructions for pre-fabricated
bookshelves. Suppose that tab A varies in size according to a Normal distribution with a mean of 30
mm and a standard deviation of 0.5 mm. The size of slot B is also Normally distributed, with a mean of
32 mm and a standard deviation of 0.8 mm. The two parts are randomly and independently selected for
packaging. What is the probability that tab A won’t fit in slot B?
a.)
b.)
c.)
d.)
e.)
3.
0.0007
0.0170
0.0618
0.9382
0.9830
Each day, Mr. Bayona chooses a one-digit number from a random number table to decide if he will walk
to work or drive that day. The numbers 0 through 3 indicate he will drive, 4 through 9 mean he will
walk. If he drives, he has a probabilty of 0.1 of being late. If he walks, his probability of being late rises
to 0.25. Find the probability that he is late. Find the probability that he is late, given that he walks.