QMB 2100 Basic Business Statistics – Spring 2014
Midterm #2 – 03/31/14
1. If A and B are independent events, with ( )
( )
, then (
)
a) equals
b) equals
c) equals
d) cannot be determined from the given information
2.
a)
b)
c)
d)
)
( )
The expression (
A and B are independent
A and B are mutually exclusive
A and B are dependent
none of the above
( ) is valid if:
3. Which of the following may be true if A and B are dependent events?
(
)
a)
( )
b) ( )
(
)
c)
d) ( ⁄
( ))
4.
a)
b)
c)
d)
Two probabilities may be multiplied when we are asked:
an ‘or’ question and the events are independent
an ‘or’ question and the events are mutually exclusive
an ‘and’ question and the event are independent
an ‘and’ question and the events are mutually exclusive
5.
a)
b)
c)
d)
If A is the event “tomorrow” it will rain” and B is the event “I will win at lottery” then
A and B are mutually exclusive and independent
A and B are neither mutually exclusive but not independent
A and B are mutually exclusive but not exclusive
A and B are independent but not mutually exclusive
6. If A and B are independent event then:
(
)
a.
(
)
( ) ( )
b.
(
)
( )
c.
( )
( )
d. ( )
1
(
7. If
)
, and
( ⁄ )
then ( ) is equal to:
a.
b.
c.
d. cannot be determined from the given information
8.
a)
( | ) is equal to
{(
b)
c)
(
d)
(
9.
a)
b)
c)
d)
)}
( )
(
)
) ( )
( )
)
( )
Given that event E has a probability of 0.25, the probability of the complement of event E
cannot be determined with the above information
can have any value between zero and one
must be 0.75
is 0.25
10. If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A|B) =
a) 0.209
b) 0.000
c) 0.930
d) None of the other answers is correct.
11. If P(A) = 0.80, P(B) = 0.65, and P  A  B   0.78 , then P(B|A) =
a)
b)
c)
d)
0.6700
0.8375
0.9750
Not enough information is given to answer this question.
12. If P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) is
a) 0.00
b) 0.25
c) 1.00
d) cannot be determined from the information given
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13. If A and B are independent events with P(A) = 0.40 and P(B) = 0.55, then P(A ∩ B) =
a) 0.76
b) 1.00
c) 0.22
d) 0.20
14. Events A and B are mutually exclusive. Which of the following statements is also true?
a) A and B are also independent.
b) P(A U B) = P(A)P(B)
c) P(A U B) = P(A) + P(B)
d) P(A ∩ B) = P(A) + P(B)
15. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A|B) =
a) 0.05
b) 0.0325
c) 0.65
d) 0.8
16. If a coin is tossed three times, the likelihood of obtaining three heads in a row is
a) zero
b) 0.500
c) 0.875
d) 0.125
17. If a penny is tossed four times and comes up heads all four times, the probability of heads on
the fifth trial is
a) zero
b) 1/32
c) 0.50
d) larger than the probability of tails
18. If P(A ∩ B) = 0,
a) P(A) + P(B) = 1
b) either P(A) = 0 or P(B) = 0
c) A and B are mutually exclusive events
d) A and B are independent events
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19. If P(A|B) = 0.20,
a) P(B|A) = 0.80
b) P(AC|B) =0 .80
c) P(A|BC) = 0.80
d) P(AC|BC) = 0.80
20.
If A and B are independent events with P(A) = 0.10 and P(B) = 0.40, then
a) P(A ∩ B) = 0.
b) P(A ∩ B) = 0.04
c) P(A  B) = 0.50
d) P(A ∩ B) = 0.25
21. If P(A) = 0.60, P(B) = 0.30, and P(A ∩ B) = 0.20, then P(B|A) =
a) 0.33
b) 0.50
c) 0.67
d) 0.90
22. A committee of 4 is to be selected from a group of 12 people. How many possible committees
can be selected?
a) 495
b) 95
c) 59
d) 120
The results of a survey of 800 married couples and the number of children they had is shown in
Table 1.
Table 1
Number
of Children
0
1
2
3
4
5
Probability
0.050
0.125
0.600
0.150
0.050
0.025
23. If a couple is selected at random, what is the probability that the couple will have less than 4
children?
a) 0.925
b) 0.225
c) 0.75
d) 0.15
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24.If a couple is selected at random, what is the probability that the couple will have more than
2 children?
a) 0.925
b) 0.225
c) 0.75
d) 0.15
25. If a couple is selected at random, what is the probability that the couple will have either 2 or
3 children?
a) 0.925
b) 0.225
c) 0.75
d) 0.15
Table 2 shows the number of students in three different degree programs and whether they are
graduate or undergraduate students:
Table 2
Degree Program
Business
Engineering
Arts & Sciences
Total
Undergraduate
150
150
100
400
Graduate
50
25
25
100
Total
200
175
125
500
26.Based on the information in Table 2, what is the probability that a randomly selected student
is and undergraduate?
a) 0.80
b) 0.35
c) 0.375
d) 0.10
27. Based on the information in Table 2, what proportion of students is engineering majors?
a) 0.80
b) 0.35
c) 0.375
d) 0.10
28.Based on the information in Table 2, if we know that a selected student is an undergraduate,
what is the probability that he or she is a business major?
a) 0.80
b) 0.35
c) 0.375
d) 0.10
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29.Based on the information in Table 2, what is the probability that a student enrolled in the
Arts and Sciences school is an undergraduate student?
a) 0.80
b) 0.35
c) 0.375
d) 0.10
30.
If P(A) = 0.35, P(B) = 0.85, and P(A ∩ B) = 0.43; then P(A  B) =
a) 1.21
b) 0.77
c) 0.68
d) 1.78
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Useful Formulas
P  A  B   P  A  P  B   P  A  B 
General Addition Rule
P  A | B 
P  A  B
P  B
P B | A 
P  A  B
P  A
Conditional Probability
a
p

b 1 p
a
p
ab
P  A  B   P  A * P  B | A 
Odds and Probabilities
General Multiplication Rule
P  A  B   P  B  * P  A | B
P  A  B   P  A * P  B 
Multiplication Rule for Independent Events
n
n!
 
 x  x ! n  x  !
n
n x
P  x     p x 1  p 
 x
Combination
Binomial Distribution
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ANSWER KEY
1. A
2. B
3. B
4. C
5. D
6. B
7. B
8. D
9. C
10. D
11. B
12. D
13. C
14. C
15. A
16. D
17. C
18. C
19. B
20. B
21. A
22. A
23. A
24. B
25. C
26. A
27. B
28. C
29. A
30. B
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