Answer the Following Problems
Problem No# 1 :
The table below lists the results of a student survey pertaining to favorite
ethnic foods. Each student chose only one type of ethnic food for the survey.
Type
Italian Chinese Japanese Thai Mexican Other
15
20
3
4
Number
Using the given table find the probability that
a) a student's favorite ethnic food is Chinese, and
b) a student's favorite ethnic food is Mexican.
ANSWER
A) probability it will be Chinese = 20/82
B) probability it will be Mexican = 30/82
30
10
Problem No# 2
An experiment with three outcomes has been repeated 50 times, and E1
occurred 20 times E2 occurred 13 times and E3 occurred 17 times. Assign
probability to the outcomes?
ANSWER
P(E1) = 20/50
P(E2) = 13/50
P(E3) = 17/50
Problem No# 3
Assume one or more 6-side dice that are fair (each of the 6 sides is equally
likely to turn up):
i. When a die is thrown, what is the probability of a 4?
ii. When a die is thrown, what is the probability that the result will be either
2 or 5?
iii. When a die is thrown, what is the probability that the result is an even
number?
ANSWER
A) P(4)= 1/6
B) P(2 or 5) = 1/6+1/6
C) P(even) = 3/6
MANAGEMENT SCIENCE-1
ABI-201
A.Aziz Al-Saadi
Problem No# 4
The manager of a large apartment complex provides the following subjective
probability estimate about the number of vacancies that will exist next month.
0
1
2
3
4
5
Vacancies
0.05 0.15 0.35 0.25 0.10 0.10
Probabilities
List the sample points in each of the following events and provide the
probability of :i. No vacancies
ii. At least four vacancies
iii. Two or few vacancies
Answer
a) 0.05
b) 0.1+0.1 = 0.2
c) 0.35+0.15+0.05
Problem No# 5
Using a regular deck of 52 playing cards, what is the probability of each of the
following:
 Drawing an ace
 Drawing a card that has a value less than eight
Answer
a) there is 4 ace in 52 cards P(ace)=4/52
b) all alternative number that could drawns = 7 four times +6
four times +5 four times + 4 four times + 3 four times + 2
four times + 1 four times = 7*4 = 28 time from all 52
It will be 28/52
Problem No# 6
In school where all students take Math and English, 80% of the students pass
Math, 93% of the students pass English, and 4% of the students fail both.
 What percentages of students fail either Math of English or both?
P( faill in math) = 100 – 80 = 20%
P( fail in English) = 100 -93 = 7%
P(fail in both) = 4%
percentages of students fail either Math of English or both =
p (fail in math union fail in English)
p ( f math union f English ) = p(f math) + p(f English) – p(fail in both)
= 0.2 + .07 - .04 = 0.23
MANAGEMENT SCIENCE-1
ABI-201
A.Aziz Al-Saadi
Problem No# 7
A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class
passed the first test. What percent of those who passed the first test also passed the second test?
ANSWER
P(BOTH)= 0.25
P(FIRST)= 0.42
P(SECOND/FIRST) = 0.25/0.42
Problem No# 9
At Kennedy Middle School, the probability that a student takes Technology and Spanish is
0.087. The probability that a student takes Technology is 0.68. What is the probability that a
student takes Spanish given that the student is taking Technology?
BOTH 0.087
TECH 0.68
P(S/TECH)= BOTH/TECH = 0.087/.68
Problem No# 10
In New York State, 48% of all teenagers own a skateboard and 39% of all teenagers own a
skateboard and roller blades. What is the probability that a teenager owns roller blades given
that the teenager owns a skateboard?
P(SKATE0= .48
BOTH = 0.39
P(ROL/SK)= BOTH/SK=0.39/.48
Problem No#11
At a middle school, 18% of all students play football and basketball and 32% of all students
play football. What is the probability that a student plays basketball given that the student plays
football?
= .18/.32
Problem No#12
In the United States, 56% of all children get an allowance and 41% of all children get an
allowance and do household chores. What is the probability that a child does household chores
given that the child gets an allowance?
= .41/.56
Problem No#13
In Europe, 88% of all households have a television. 51% of all households have a television and
a VCR. What is the probability that a household has a VCR given that it has a television?
0.51/0.88
MANAGEMENT SCIENCE-1
ABI-201
A.Aziz Al-Saadi
Problem NO#14
Many school systems now provide internet access for their students. At 2008 internet access
was provided at 21733 elementary schools, 7286 junior schools, and 10682 high school the
total number of school includes 51745 elementary school, 14012 junior high schools, and
17229 high schools answer the following questions:a) If you randomly choose an elementary school to visit, what is the probability it will
have internet access? = 21733/517145
b) If you randomly choose a junior high school to visit, what is the probability it will have
internet access? 7286/14012
c) If you randomly choose a school to visit, what is the probability it will be an
elementary school? 51745/(TOTAL NUMBER OF SCHOOL)
d) If you randomly choose a school to visit, what is the probability that it will have
internet access? SUM ALL INTERNET ACCESS/ TOTAL NUMBER OF SCHOOL
Problem NO# 18
In a survey in MBA students, the following data were obtained on students first reason for
application to the school in which they matriculated.
Reason for application
Enrolment
Status
School
Quality
School
Cost
Other
Reason
Full time
421
393
76
890
Part Time
400
593
46
1039
Totals
821
986
122
1929
Totals
a) Develop a Joint probability table using these data?
b) Use the marginal properties of school quality and school cost and other to comments on
the most important reason for choosing a school?
c) If a student goes full time what is the probability that school quality will be the first
reason for choosing a school?
d) If a student goes part time what is the probability that school quality will be the first
reason for choosing a school?
ANSWER
A)
Reason for application
School
Quality
Enrolment
Status
School
Cost
Other
Reason
Totals
Full time
421/1929
393/1929
76/1929
890
Part Time
400/1929
593/1929
46/1929
1039
Totals
821/1929
986/1929
122/1929
1929
MANAGEMENT SCIENCE-1
ABI-201
A.Aziz Al-Saadi
MANAGEMENT SCIENCE-1
ABI-201
A.Aziz Al-Saadi