Question

At a certain university, 140 of the 200 employees are Lebanese.
Of the Lebanese employees, 40% are fluent in English, 50% are
fluent in French, and the rest are fluent in Spanish. Of the
non-Lebanese employees, 70% are fluent in English, 20% are fluent
in French, and the rest are fluent in Spanish.

1. Draw a probability tree diagram

2. Find the probability that a randomly selected employee is
non-Lebanese and fluent in English

3. Given that a randomly selected employee is fluent in English,
find the probability that (s)he is nonLebanese

Answer #1

1. In a certain population, 26% of the persons smoke
and 9% have a certain type of heart disease.Moreover, 14% of the
persons who smoke have the disease.
(a) What percentage of the population smoke and have
the disease?
(b) What percentage of the population with the disease
also smoke?
2. At a certain university in the United States, 64%
of the students are at least bilingual{speaking English and at
least one other language. Of these students, 79% speak Spanish...

Solve the problem
A random sample of 140 employees in a textiles manufacturing
company was
chosen in order to determine their retirement plan after age 65.
Those selected in
the sample were divided into management and production. The
results were:
Plans after Age 65
__________________________________________________________________
Employee Retire (R) Not Retire (N) Total
__________________________________________________________________
Management (M) 70 20 90
Production (P) 32 18 50
Total 102 38 140
__________________________________________________________________
Suppose that an employee is selected at random from this group.
Find...

Suppose that a large corporation offers its employees two health
plans: a 70/30 plan with high deductible and an 80/20 plan with low
deductibles. Every employee has one plan or the other. Of all
employees, 75% are production workers and 25% are administrative
workers. Of all employees, 35% choose 70/30 plan. Of all production
workers, 40% choose the 70/30 plan.
A. What is the probability that randomly selected employee will
be administrative employee?
B. What is the probability that a...

A certain company sends 40% of its overnight mail parcels via
express mail service E1. Of these parcels, 2% arrive after the
guaranteed delivery time (denote the event late delivery by L).
Suppose that 50% of the overnight parcels are sent via express mail
service E2 and the remaining 10% are sent via E3. Of those sent via
E2 on 5% arrive late, whereas 1% of the parcels handled by E3
arrive late.
Part a: Draw a tree diagram for...

Employees of a local university have been classified according
to gender and job type. If an employee is selected at random, what
is the probability that the employee is a member of the hourly
staff, given that the employee is female?
Job Male Female
Faculty(FA) 110 10
Salaried Staff(SS) 30 50
Hourly Staff (HS) 60 40
A 0.400 B 0.133 C 0.160 D 0.053 E 0.533

Employees of a local university have been classified according
to gender and job type.
Male
Female
Faculty
110
60
Salaried Staff
50
60
Hourly Staff
80
40
If an employee is selected at random, what is the probability that
the employee is a member of the hourly staff given that the
employee is male?
0.124
0.235
0.260
0.286
0.333
If the scores on an aptitude test are normally distributed with
mean 600 and standard deviation 50, what proportion of the...

A small manufacturing company has 340 employees (excluding top
management) classified as supervisors, professional staff, and blue
collar workers. It is known that there are 20 supervisors, and 70%
of all employees are blue collar workers. Two percent of
supervisors, 40% of professional staff, and 74% of blue collar
workers are union members. Construct a contingency table given the
above data.
a- What percentage of workers are union members?
b- If a random union member employee is selected, what is...

An alcohol awareness task force at a Big-Ten university sampled
200 students after the midterm to ask them whether they went bar
hopping the weekend before the midterm or spent the weekend
studying, and whether they did well or poorly on the midterm. The
following result was obtained.
Did Well on Midterm
Did Poorly on Midterm
Studying for Exam
80
20
Went Bar Hopping
30
70
Using the Table above,
(a) Suppose a randomly selected student who went bar hopping,...

Antibodies against COVID-19 have 90% chance of
preventing reinfection. Probability of getting infected and sick
without antibodies is 50%. It is estimated that in a country 25% of
all people have COVID-19 antibodies.
a) If a person is selected at random, find the
probability that (s)he is at the danger of contracting the
disease.
b) Draw Venn’s diagram and decision tree for the
situation. Explain.

Exercise 5.11. Sex and switching majors. At a certain
university, 60% of undergraduate students are male, and 40% are
female. Ten percent of females change their majors at least once.
Overall, 30% of students change their majors at least once. a. Find
the probability that, given a randomly selected student who changes
majors, the student is a female. b. What percentage of males change
their majors at least once?

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