Submit your responses to the following prompts.
A
midsized company recently divided all employees into four divisions.
Division 1 makes up 43% of the company, Division 2 makes up 40%, Division
3 makes up 12%, and Division 4 makes up 5%. Choose one employee at random.
Find the probability for each of the following statements. (75 words, or 1
paragraph)
The
employee belongs to Division 1.
The
employee belongs to either Division 2 or Division 3.
The
employee does not belong to Division 1 or Division 2.
Jasmine
Robbins wants to open an independent coffee shop in a town that already
has 9 coffee shops: 3 Mocha Moose, 2 Elkhorn Coffee, and 4 Morning JoJo.
She is trying to determine the probability of choices that potential
customers may make. Here is one of her questions: If a person selects one
shop at random to purchase coffee, find the probability that it is either
a Mocha Moose or a Morning JoJo. Explain your answer. (75 words, or 1
paragraph)
The
following chart shows the number of customer complaints from three regions
of an organization for two separate years.
2018
2017
Northeast
region
6,493
3,401
Southeast
region
732
2,513
Central
region
3,706
1,082
Find the probability for each
question. (75 words, or 1 paragraph)
What
is the probability that a complaint was from the Southeast region, given
it was in 2017?
What
is the probability that a complaint was from the Central region, given it
was in 2018?
What
is the probability that a given complaint did not occur in 2018 and was
not from the Southeast region?
What
is the probability that two complaints chosen at random were both from
the Northeast region?
A
management consulting team needs a team of four to analyze the operations
of a new client. The team should comprise an accountant, a production
specialist, a finance specialist, and a management specialist. On its
staff, the consulting firm has available six accountants, five production
specialists, three finance specialists, and eight management specialists.
How many different teams could be formed from the available individuals?
(75 words, or 1 paragraph)
In a
batch of 20 television picture tubes, 5 are known to be defective. What is
the probability that a random sample of 5 (without replacement) will
result in each of the following? (75 words, or 1 paragraph)
Exactly
1 defective
No
defectives
Two
or fewer defectives
The
board of directors for a particular company consists of 10 members, 6 of
whom are loyal to the current company president and 4 of whom want to fire
the president. Suppose the chair of the board (who is a loyal supporter of
the current president) suggests to randomly select 4 other board members
to serve on a committee to decide the president’s fate. Find the
probability for the first 3 questions and explain your answer for the
fourth question. (75–150 words, or 1–2 paragraphs)
What
is the probability that all 5 committee members will vote to keep the
president in place, if no one changes their minds?
What
is the probability that a majority of the committee will vote to keep the
president in place, if no one changes their minds?
What
is the probability that the vote is 4 to 1 to replace the president, if
no one changes their minds?
Imagine
that you were the president of the company and you hoped to keep your
position. Considering the various probabilities, would you consider the
chair of the board’s suggestion to be in your favor or not? If the choice
was yours, would you allow the suggestion to proceed?
Dave
has just left an interview with a prospective employer. The hiring manager
told Dave that she will tolerate one mistake during his first year but will
fire him if he makes two mistakes. Based on Dave’s research and
understanding of the job, he estimates that he will have to make five
critical decisions during the year, and with his knowledge of the
processes, figures that he will have about an 80% chance of making any of
those five decisions correctly. Dave does not want to run any more than a
25% chance of being fired. If each of the decisions is independent of the
others, should Dave risk taking the job if offered? Explain why or why
not. (75 words, or 1 paragraph)
For each prompt, be sure to reference at least
one scholarly source to support your answer. Use the Template provided please.
