1.
(6 pts) Match the statement with Venn diagram available from this link: Venn Diagrams
The shaded area meets the description:
a. The set of all objects with characteristics B and C but not A. D
b. The set of all objects with characteristics B or C but not A. B
c. The set of all objects with exactly two of the characteristics. E
d. The set of all objects with exactly one characteristic. None
2.
(6 pts) An experiment consists of choosing a subset from a fixed number of objects where the arrangement of the chosen
objects is not important. Determine the size of the sample space when you choose the following:
a.
4 objects from 15: C(15, 4) = 1365
b.
5 objects from 14: C(14,5) = 2002
c.
9 objects from 18: C(18,9) = 48620
3.
(3 pts) Suppose you are managing 14 employees, and you need to form three teams to work on different projects. Assume
that all employees will work on a team, and that each employee has the same qualifications/skills so that everyone has the
same probability of getting chosen.
How large is the sample space for all ways the teams be chosen so that the number of employees on each project are as
follows:
7 on Team 1 and 3 on Team 2 and 4 on Team 3
C(14, 7)* C(7, 3)*C(4, 4) = 120120
4. (4 pts) Determine whether the following are valid probability models or not. Type º”VALID” if it is valid, or type “INVALID”
if it is not.
Useful Short Cut: If a word is spelled on this page it can be highlighted and copied or dragged and dropped into a box. Try it with
Valid.
i.
Event
e1 e2 e3
e4
Probability
0.1
0
0.7
0.2
VALID. It adds to one and has values from 0 to 1.
ii.
Event
e1
e2
e3 e4
Probability
0.1
0.2
0.3 1
INVALID. It adds to more than one.
5.
(4 pts) If
, find:
i.
ii.
The odds FOR E. 1 to 2
The odds AGAINST E. 2 to 1
iii.
The probability AGAINST E.
6. (2 pts) Four weather guessers were preparing for the evening news. After much thought and use of a dart board, they state
“The probability of rain is
7.
”. “What are the odds against rain? 2 to 9
(6 pts) The sample space for an experiment contains five sample points or outcomes. The probabilities of the sample points
are:
P(1) = P(2) = 0.17
P(3) = P(4) = 0.19
P(5) = 0.28
Find the probability of each of the following events:
A : { Either 2 or 5 occurs }
B : { Either 2 ,1, or 4 occurs }
C : { 3 does not occur }
P(A) =0.45 = 0.17 + 0.28
P(B) = 0.53 = 1 - (0.19 + 0.28)
P(C) =0.81= 1 - 0.19
8. (10 pts) In a survey of 141 people, the following incomplete data were obtained relating gender to color-blindness:
Complete the table then answer the following information.
Color-Blind (C)
Not Color - Blind (C)
Total
Male (M)
70
29
99
Female (F)
27
15
42
Total
97
44
141
Parts a - d deal with probability using the table. A person is randomly selected. What is the probability that the person is:
a.
Male?
b.
Male and Color-blind?
c.
Male given that the person is Color-blind?
d.
Color-blind given that the person is Male?
(6 pts) Consider the experiment composed of randomly rolling a fair die marked with the following numbers: 1, 2, 3, 4, 5, 6
followed by flipping of a fair coin marked H and T one time.Determine the probability of each of the following events:
A : { A T appears on the coin. } P(A) = 0.5
B : { An even number appears on the die; an H appears on the coin. } P(B) = 0.5*0.5 = 0.25
9.
C : { A 5 appears on the die; an H appears on the coin. } P(C) =
D : { An odd
number appears on the die. } P(D) = 0.5
10. (12pts) Find each probability by referring to the tree diagram above.
a. P(C|A) = 0.55
b. P(D|B) =0.25
c. P(A 1 C) = 0.22
d. P(B 1 D) = 0.15
e. P(C) = 0.67
f. P(D) =0.33