AU Rule of Probabilities Questions

The purpose of this assignment is to give us experience with the mechanics of probabilities,and with applying probability to different types of management and policy questions.
Complete the following exercises:
1. A computer network is mostly reliable but does experience occasional interruptions
during the day. If there are two or more interruptions in a single day the system must
be rebooted and data are sometimes lost.
Over a long period of time the following data have been collected:
Interruptions
per Day
0
1
2
3
4
5
Frequency
0.35
0.25
0.20
0.10
0.05
0.05
Let A be the event “there will be at least two interruptions” and let B be the event
“there will be fewer than 4 interruptions.
a) Find the probability of A
b) Find the probability of B
c) Find the probability of the complement of A
d) Find the probability of the intersection of A and B
e) Find the probability of the union of A and B
2.
The Molecular Engineering program is reviewing their admissions criteria. Based
on a few years’ worth of data, they find they admit roughly 33% of all applicants.
Of females who apply, roughly 59% are denied admission. Of males, 30% who
apply are admitted. Of all applicants, 76% are male.
Define the events and their complements.
a) What is the probability that a randomly selected applicant is male?
b) What is the probability that a randomly selected individual is an admitted female?
c) Does knowing if an applicant is female change your prediction of whether
an applicant is admitted? Show why and explain in one sentence.
3.
In a large federal agency, 45% of the employees are men and 55% are women. The
highest levels of education obtained by the male employees are graduate degree
(20%), undergraduate degree (60%), and high school diploma (20%). In comparison,
25% of the female employees have a graduate degree, 55% have an undergraduate
degree, and 20% have a high school diploma.
a) Find the probability that a randomly chosen employee will have a graduate degree.
b) What is the probability that a randomly chosen employee who has a graduate degree
is a woman?
c) Are gender and level of education of employees in this agency independent?
d) What is the probability that a randomly chosen employee who has not had a
graduate degree is a man?
4.
A survey of residents in a medium-sized metropolitan area provides the following data
on the number of crimes that go unreported:
Type of
Crime
Report
ed
Not
Reported
Total
Murder
21
0
21
Robbery
134
142
276
Assault
Rape
56
15
214
63
270
78
Auto theft
335
34
369
Total
561
453
1014
As an advocate for a violence prevention program, write a short paragraph (100 words or
less) summarizing the probability that crimes go unreported, both overall and for specific
crimes. [Hint: Which crimes are most likely to go unreported, and which are least likely
to go unreported?
Use the following table to answer the following questions:
1. What is the probability that someone has health insurance?
2. What is the probability that someone has health insurance and received food stamps?
3. What is the probability that someone who is not receiving food stamps had health
insurance?
4. If someone has health insurance, what is the probability that they receive food stamps?
5. If someone receives food stamps, what is the probability they also have health insurance?
6. Based on the table, do you think receiving food stamps is independent of whether a
person also has health insurance? Use an independence test to demonstrate your rationale
and explain in one sentence.