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
Number / 15 / 20 / 3 / 4 / 30 / 10
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
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
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.
Vacancies / 0 / 1 / 2 / 3 / 4 / 5
Probabilities / 0.05 / 0.15 / 0.35 / 0.25 / 0.10 / 0.10
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:
Ø Drawing an ace
Ø 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.
Ø 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
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
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 applicationSchool / School / Other Reason / Totals
Quality / Cost
Enrolment
Status / Full time / 421 / 393 / 76 / 890
Part Time / 400 / 593 / 46 / 1039
Totals / 821 / 986 / 122 / 1929
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 applicationSchool / School / Other Reason / Totals
Quality / Cost
Enrolment
Status / 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