Use the following information to answer questions 1 -2
From an urn containing 5 red balls, 3 white balls and 7 blue balls, 3 are drawn successively.
1.
The probability that they are drawn in the order red, white, blue, if sampling is done with
replacement is:
a. 0.9671
b. 0.2511
c. 0.0311
d. 0.3011
2. The probability that they are in the order red, white, blue, if sampling done without
is
replacement
b. 0.4671
b. 0.2554
c. 0.0311
d. 0.0385
Use the following information to answer questions 3 – 5
A carton of 25 transistor batteries has 5 defectives. Three transistors are drawn without
replacement.
3. What is the probability that all three batteries drawn will be defective?
a. 0.1078
b. 0.0069
c. 0.0043
d. 0.0.062
4. What is the probability that the first battery is non-defective and the second is defective?
a. 0.167
b. 0.833
c. 0.621
d. 0.211
5. What is the probability of at least one battery in the sample will be defective?
a. 0.504
b. 0.496
c. 0.283
d. 0.510
Use the following information to answer questions 6 –8
A car dealer wishes to sell two cars, a BMW and a Mercedes. On any given day, the
probability that he sells the Mercedes is 0.03. The probability that he sells the BMW is 0.05.
The probability that he sells both the Mercedes and the BMW is 0.02. What is the
probability that the car dealer:
6. sells the buy Mercedes or BMW?
a. 0.1
b. 0.9
c. 0.02
d. 0.06
7. sells the BMW and not Mercedes?
a. 0.04
b. 0.03
c. 0.12
d. 0.015
8. sells one of the two cars?
a. 0.06
b. 0.02
c. 0.5
d. 0.04
Use the following information to answer questions 9-10
If 𝑃𝑃(𝐴𝐴 ∪ 𝐵𝐵) = 0.8 and 𝑃𝑃(𝐴𝐴) = 0.4 and 𝑃𝑃(𝐵𝐵) = 𝑝𝑝.
9. Find 𝑃𝑃(𝐵𝐵) if 𝐴𝐴 and 𝐵𝐵 are mutually exclusive (or disjoint).
a. 0.55
b. 0.4
c. 0.5
d. 0.45
10. Find 𝑃𝑃(𝐵𝐵) if 𝐴𝐴 and 𝐵𝐵 are independent events.
a. 0.67
b. 0.33
c. 0.50
d. 0.35
Use the following information to answer questions 11 – 15
Three hundred employees from MSC were cross-classified on the basis of age and work category. The
information is summarized in the following table.
Work category →
Production
Sales
Office
Total
Age ↓
<25
50
2
50
102
25-40
70
24
50
144
>40
40
4
10
54
Total
160
30
110
300
11. Find the probability that the employee is a sales person and between 25 and 45 years of age.
a. 0.08
b. 0.92
c. 0.45
d. 0.38
12. Find the probability that a randomly selected employee is under 25 years of age.
a. 0.66
b. 0.38
c. 0.34
d.
0.33
13. The probability that the employee is over 40, given that she/he is an office worker is:
a. 0.251
b. 0.053
c. 0.033
d. 0.091
14. Find the probability that the employee is a production worker or under 25, or both.
a. 0.707
b. 0.293
c. 0.821
d. 0.293
15. Find the probability that the employee is a production worker.
a. 0.173
b. 0.367
c. 0.467
d. 0.533
Use the following information to answer questions 16 -17
A manufacture makes writing pens. The manufacturer employs an inspector to check the quality of his
product. The inspector tested a random sample of the pens from a large batch and calculated that the
probability of any pen being defective is 0.025. Amanda buys two of the pens made by the manufacture.
16. The probability that both pens are defective is:
a.
b.
c.
d.
0.000625
0.006250
0.052500
0.905000
17. The probability that exactly one of the pens is defective is:
a. 0.10005
b. 0.04875
c. 0.00255
d. 0.99755
18. In how many ways can 7 people be arranged in a line?
a. 6
b. 7
c. 5040
d. 720
19 In how many different arrangements can three red, four yellow and two blue bulbs be arranged on a
string of Christmas tree lights that contains nine sockets?
a. 1260
b. 9
c. 3! × 4! × 2!
d. 24
20. How many distinguishable arrangements are there of the letters in “HIPPOPOTAMUS”?
a. 3 × 2 × 1 = 6
b. 3! × 2! × 3! = 72
c. 12!
d. 39916800
21. A team of 4 children is to be selected from a class of 20 children, to compete in a quiz team. In how
many ways can a team be chosen if any four can be chosen?
a. 4845
b. 116 280
c. 80
d. 160
22. A sport committee at the local hospital consists of 5 members. A new committee is elected, of which
3 members must be women and 2 members must be men. How many different committees can be
formed if there were originally 5 women and 4 men to select from?
a. 60
b. 20
c. 100
d. 6
Use the following information for questions 23 and 24
Find the number of three-digit numbers that can be formed when taken from {1,2,3,4,5,6,7,8,9}, if
23. the three digits are all different.
a. 504
b. 729
c. 900
d. 27
24. the three digits are all the same.
a. 729
b. 9
c. 504
d. 27
Use the following information to answer questions 25 – 27
Consider only the picture cards namely Kings, Queens, Jacks from a pack of cards. There are 4 suits
namely hearts (red), diamonds (red), clubs (black) and spades (black). Suppose 4 cards are drawn
without replacement from the 12 cards.
25. What is the probability of drawing 3 Kings and 1 Jack?
a. 0.0323
b. 0.0056
c. 0.0121
d. 0.0727
26. What is the probability of all 4 cards being black?
a. 0.5
b.
1
×
1
6
×
5
6
×
5
c. 0.0303
d.
12
12
1
4
×
×
4
12
1
3
×
3
12
27. What is the probability that 2 King, 1 Queens and 1 Jack are drawn?
a. 0.1939
b.
c.
d.
1
4
4
12
4
×
×
12
2
2
4
12
×
×
1
4
1
12
Use the following information to answer questions 28- 30
Consider the following probability distribution
x
1
2
3
4
5
P(x)
0.2
0.25
0.4
k
0.05
28. What is the value of k?
a. 0.4
b. 0.1
c. 0.75
d. 0.3
29. The value of the mean, 𝜇𝜇 is
a. 3
b. 2.25
c. 2.55
d. 2.85
30. The value for 𝑃𝑃(𝑋𝑋 ≥ 4) is
a. 0.1
b. 0.15
c. 0.65
d. 0.5
31. The value of Σ 𝑥𝑥 2 𝑃𝑃(𝑥𝑥) is
a. 6.95
b. 7.56
c. 6.5
d. 7.65
32. The variance, 𝜎𝜎 2 is
a. 0.6545
b. -0.0455
c. 1.1525
d. 1.1475
Use the following information for questions 33- 35
Suppose the random variable 𝑋𝑋 has the following probability distribution:
33. Find the value of 𝑐𝑐.
a.
b.
c.
d.
𝑃𝑃(𝑋𝑋 = 𝑥𝑥) = 𝑐𝑐 (𝑥𝑥 2 ),
1
18
1
21
1
91
1
22
34. The value of 𝑃𝑃(𝑋𝑋 = 2) is
a.
b.
c.
d.
4
91
1
2
3
10
3
13
35. The mean, 𝜇𝜇 is
a. 3.55
b. 4.52
c.
63
13
d. 2.45
𝑥𝑥 = 1, 2, 3, 4, 5, 6.
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FORMULAE
1. 𝑃𝑃(𝐴𝐴|𝐵𝐵) =
𝑃𝑃(𝐴𝐴∩𝐵𝐵)
𝑃𝑃(𝐵𝐵)
, 𝑃𝑃(𝐵𝐵) ≠ 0.
2. 𝑃𝑃(𝐴𝐴 ∪ 𝐵𝐵) = 𝑃𝑃(𝐴𝐴) + 𝑃𝑃(𝐵𝐵) − 𝑃𝑃(𝐴𝐴 ∩ 𝐵𝐵)
3. De Morgan’s Laws
��������
𝐴𝐴
∪ 𝐵𝐵 = 𝐴𝐴̅ ∩ 𝐵𝐵�
��������
𝐴𝐴
∩ 𝐵𝐵 = 𝐴𝐴� ∪ 𝐵𝐵�
4. 𝜇𝜇 = Σ 𝑥𝑥 𝑃𝑃(𝑥𝑥)
5. 𝜎𝜎 2 = Σ 𝑥𝑥 2 𝑃𝑃(𝑥𝑥) − 𝜇𝜇2
6.
𝑛𝑛!
𝑥𝑥1 !× 𝑥𝑥2 !×…× 𝑥𝑥𝑘𝑘 !
TEST 2 SOLUTION
1. b
2. d
3. b
4. b
5. c
6. c
7. a
8. c
9. b
10. a
11. b
12. c
13. c
14. a
15. d
16. b
17. b
18. d
19. a
20. d
21. c
22. c
23. a
24. c
25. d
26. c
27. a
28. b
29. c
30. d
31. a
32. a
33. b
34. c
35. d