Test 4
1
Assume that the probability of a woman giving birth to a female child is 0.55 and that
only female and male children can be born to a woman. Assume that the sex of one child
is independent from the sex of another child on separate births. A woman has 6 separate
births. What is the probability that she gives birth to 4 males?
a)
4
6
6
b)  (0.55) 4 (1  0.55) 2
 4
6
c)  (0.55) 2 (1  0.55) 4
 4
6
d)  (0.55) 6 e) none of these
 4
Assume that the probability of a woman giving birth to a female child is 0.55 and that
only female and male children can be born to a woman. Assume that the sex of one child
is independent from the sex of another child on separate births. A woman has 7 separate
births. What is the probability that she gives birth to 3 males?
a)
7
3
7
b)  (0.55) 3 (1  0.55) 4
3
7
c)  (0.55) 4 (1  0.55) 3
3
7
d)  (0.55) 7 e) none of these
3
Assume that the probability of a woman giving birth to a female child is 0.55 and that
only female and male children can be born to a woman. Assume that the sex of one child
is independent from the sex of another child on separate births. A woman has 9 separate
births. What is the probability that she gives birth to 2 females?
a)
9
2
9
b)  (0.55) 2 (1  0.55) 7
 2
9 
c)  (0.55) 7 (1  0.55) 2
 2
9 
d)  (0.55) 9 e) none of these
 2
_____________
2.
A multiple choice exam has 30 questions. Each question has 3 choices, of which exactly
one is the right answer. A person answer this exam randomly. What is the probability of
scoring exactly13 correct?
 30  1
2
a)  ( )13 ( )17
3
13  3
 30  1
2
b)  ( )17 ( )13
3
13  3
c)
13
30
d) 30 
1
e) none of these
13
A multiple choice exam has 30 questions. Each question has 4 choices, of which exactly
one is the right answer. A person answer this exam randomly. What is the probability of
scoring exactly13 correct?
 30  1
3
a)  ( )13 ( )17
4
13  4
 30  1
3
b)  ( )17 ( )13
4
13  4
c)
13
30
d) 30 
1
e) none of these
13
A multiple choice exam has 25 questions. Each question has 3 choices, of which exactly
one is the right answer. A person answer this exam randomly. What is the probability of
scoring exactly13 correct?
 25  1
2
a)  ( )13 ( )12
3
13  3
 25  1
2
b)  ( )12 ( )13
3
13  3
c)
13
1
d) 25 
e) none of these
25
13
___________
3.
A population consists of green people and purple people only. It is known that 20% are
green people. A jury of 12 is selected from this population. What is the probability that
the jury consist of exactly 7 purple people and 5 green people?
12 
a)  (0.2) 7
7 
12 
b)  (0.8) 7 (0.2) 5
7 
c) (0.2) 5 (0.8) 7
d)
5
e) none of these
7
A population consists of green people and purple people only. It is known that 20% are
green people. A jury of 12 is selected from this population. What is the probability that
the jury consist of exactly 9 purple people and 3 green people?
12 
a)  (0.2) 3
3 
12 
b)  (0.8) 9 (0.2) 3
9 
c) (0.2) 3 (0.8) 9
d)
3
e) none of these
9
A population consists of green people and purple people only. It is known that 40% are
green people. A jury of 12 is selected from this population. What is the probability that
the jury consist of exactly 7 purple people and 5 green people?
12 
a)  (0.4) 7
7 
12 
b)  (0.6) 7 (0.4) 5
7 
c) (0.4) 5 (0.6) 7
d)
5
e) none of these
7
_________
4
A true-or false exam has 10 questions. A person answers T, F, or leaves the question
blank. Each question has exactly one answer T or F. What is the probability that a person
obtains 7 correct answers on the exam?
10  1 2
a)  ( ) 7 ( ) 3
7  3 3
10  1
b)  ( )10
7  2
10  1
c)  ( ) 3
7  2
10  1
d)  ( ) 7 e) none of these
7  3
A true-or false exam has 12 questions. A person answers T, F, or leaves the question
blank. Each question has exactly one answer T or F. What is the probability that a person
obtains 7 correct answers on the exam?
12  1
a)  ( ) 7
7  3
12  1
b)  ( )12
7  2
12  1
c)  ( ) 5
7  2
12  1 2
d)  ( ) 7 ( ) 5 e) none of these
7  3 3
A true-or false exam has 10 questions. A person answers T, F, or leaves the question
blank. Each question has exactly one answer T or F. What is the probability that a person
obtains 8 correct answers on the exam?
10  1 2
a)  ( ) 8 ( ) 2
8  3 3
10  1
b)  ( )10
8  2
10  1
c)  ( ) 2
8  2
10  1
d)  ( ) 8 e) none of these
8  3
__________________
5.
A factory produces bolts and it is known that 1/8 of the bolts are defective. Bolts are sold
in boxes containing 25 bolts each. What is the probability that a given box will contain no
more than 1 defective bolt?
a)
1
8
1 7
7
b) 25( )( ) 24   
8 8
8
25
1 7
c) 25( )( ) 24
8 8
7
d)  
8
25
e) none of these
A factory produces bolts and it is known that 1/12 of the bolts are defective. Bolts are
sold in boxes containing 25 bolts each. What is the probability that a given box will
contain no more than 1 defective bolt?
1
a)
12
1 11
 11 
b) 25( )( ) 24   
12 12
 12 
25
1 11
c) 25( )( ) 24
12 12
 11 
d)  
 12 
25
e) none of these
A factory produces bolts and it is known that 1/8 of the bolts are defective. Bolts are sold
in boxes containing 30 bolts each. What is the probability that a given box will contain no
more than 1 defective bolt?
1
a)
8
1 7
7
b) 30( )( ) 29   
8 8
8
30
 30  1 7
c)  ( )( ) 29
1  8 8
7
d)  
8
30
e) none of these
_________
6
A multiple choice exam has 25 questions. Each question has 4 choices, of which exactly
one is the right answer. A person answer this exam randomly. What is the probability of
scoring at least 24 correct?
1
a)  
4
25
3 1
1
b) 25( )( ) 24   
4 4
4
25
1 3
3
c) 25( )( ) 24   
4 4
4
25
3
d) 1   
4
25
e) none of these
A multiple choice exam has 30 questions. Each question has 4 choices, of which exactly
one is the right answer. A person answer this exam randomly. What is the probability of
scoring at least 29 correct?
1
a)  
4
30
3 1
1
b) 30( )( ) 29   
4 4
4
30
1 3
3
c) 30( )( ) 29   
4 4
4
30
3
d) 1   
4
30
e) none of these
A multiple choice exam has 25 questions. Each question has 5 choices, of which exactly
one is the right answer. A person answer this exam randomly. What is the probability of
scoring at least 24 correct?
1
a)  
5
25
4 1
1
b) 25( )( ) 24   
5 5
5
25
1 4
4
c) 25( )( ) 24   
5 5
5
25
4
d) 1   
5
25
e) none of these
_________________
7
A deck of cards has 10 cards: 3 (identical) red and 7 (identical) blue. 5 cards are drawn at
random. What is the probability of getting at least 3 red cards. Please do not evaluate
your answer but give the answer using ‘n choose k’ expressions.
n
n
Use C(n, k) to denote  , that is C(n, k)   , also, nstead of x n you can write x^ n
k
k
A deck of cards has 12 cards: 3 (identical) red and 9 (identical) blue. 5 cards are drawn at
random. What is the probability of getting at least 3 red cards. Please do not evaluate
your answer but give the answer using ‘n choose k’ expressions.
n
n
Use C(n, k) to denote  , that is C(n, k)   , also, nstead of x n you can write x^ n
k
k
A deck of cards has 12 cards: 3 (identical) red and 9 (identical) blue. 7 cards are drawn at
random. What is the probability of getting at least 5 red cards. Please do not evaluate
your answer but give the answer using ‘n choose k’ expressions.
n
n
Use C(n, k) to denote  , that is C(n, k)   , also, nstead of x n you can write x^ n
k
k