Question

In: Math

Q #5 The computers of six faculty members in a certain department are to be replaced....

Q #5 The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2,…, 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).

a. What is the probability that both selected setups are for laptop computers?

b. What is the probability that both selected setups are desktop machines?

c. What is the probability that at least one selected setup is for a desktop computer?

d. What is the probability that at least one computer of each type is chosen for setup?

Solutions

Expert Solution

Given: There are total 6 computers faculty members.

2 of them are selected laptops and 4 of them are selected desktop

2 computers are selected from 6 that is

There are total 15 equally likely outcomes of selecting two computers.

a. P(both selected setups are for laptop computers)

That is select 2 from 2 laptops and the total are 15 possibilities.

Or we can take the probability as,

Therefore, the probability that both selected setups are for laptop computers is 1/15

b. The probability that both selected setups are desktop machines.

That has to select both desktops from 4.

Therefore, the probability that both selected setups are desktop machines is 6/15.

c. The probability that at least one selected setup is for a desktop computer.

At least one desktop means either one is desktop or both are a desktop.

There are 3 possibilities either first is desktop and second is a laptop OR first laptop and second desktop OR both are desktops.

Therefore, the probability that at least one selected setup is for a desktop computer is 14/15

d. The probability that at least one computer of each type is chosen for setup.

Only 2 have to select, so at least one of each type means both are selected that is either laptop then desktop OR desktop then a laptop.

Therefore, the probability that at least one computer of each type is chosen for setup is 8/15.

milcah answered 5 months ago

Next > < Previous

Related Solutions

Of 30 personal computers (PCs) owned by faculty members in a certain university department, 20 run...

Of 30 personal computers (PCs) owned by faculty members in a certain university department, 20 run Windows, eight have 21-inch monitors, 25 have CD-ROM drives, 20 have at least two of these features, and six have all three. a) How many PCs have at least one of these features? b) How many have none of these features? c) How many have exactly one feature?

The Business Education Department has six full-time faculty members. At their monthly department meeting, each full-time...

The Business Education Department has six full-time faculty members. At their monthly department meeting, each full-time faculty member reported the number of hours they taught during the past month: Faculty Member Teaching Hours Bernhardt 84, Haas 92, England 84, Pecord 83, Hines 92, Tanner 83 A. Calculate the population mean for the six full-time faculty members: B. If two full-time faculty members are selected randomly, how many different samples are possible? C. Calculate the sample means: D. Calculate the sampling...

Suppose that the following data represents ages of all tenured faculty members in a certain academic...

Suppose that the following data represents ages of all tenured faculty members in a certain academic department, and we want to numerically describe the age distribution for this department only: 42, 39, 44, 50, 45, 42, 36, 47, 39, 42, 43, 47 What is the 3rd quartile?

A travel agency is planning a trip to England for 100 members of a college faculty....

A travel agency is planning a trip to England for 100 members of a college faculty. The plane fare will be $600 per faculty member if all members attend the trip. With each cancellation, however l, the fare will increase by$250 per faculty member. the cost to the agency is $20,000 plus $40 for each passenger. What is the price that will generate the maximum profit for the agency?

A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The...

A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.” The paper reports this as “Professor McDaniel said that good researchers tend to be poor teachers, and vice versa.” Explain why he paper’s report is wrong. Write a statement in plain language (don’t use the word “correlation”) to explain the psychologist’s meaning....

PART I A survey with an SRS of 2500 faculty members at US universities found that...

PART I A survey with an SRS of 2500 faculty members at US universities found that on average they had published 1.7 papers the previous 2 years with anSD of 2.3 papers. Find a 95% confidence interval for the average number of papers published by faculty members at US institutions in the previous2 years. PART II In 2001, a survey was carried with a simple random sample of 500 house-holds from 25,000 households in a certain town. (a)239 of the...

The faculty of a university mathematics department is concerned about the performance of students in the...

The faculty of a university mathematics department is concerned about the performance of students in the introductory calculus offered by the department and required of all science and engineering majors. Historically, class averages on the test have been about 75, a passing grade but indicative that students may not be learning the material as well as they need to in order to go on to the next course. The chair would like to raise the average to at least 80....

Provide the AICPA code reference to the rule that requires even part time faculty members to...

Provide the AICPA code reference to the rule that requires even part time faculty members to comply with the integrity and objectivity rule.

Skyline Preparatory High for Girls is an elite prep school with 47 faculty and staff members...

Skyline Preparatory High for Girls is an elite prep school with 47 faculty and staff members on the payroll. Jamie Davis, a two-year English instructor, becomes pregnant. She is not married. She is a slim woman who is not showing visible signs of pregnancy and has not told the school administrators of her pregnancy. In her sixth month of pregnancy she develops pre-eclampsia, necessitating that she go on pregnancy leave immediately. Davis requests medical leave due to her pregnancy and...

In a certain survey, 500people chose to respond to this question: "Should passwords be replaced with...

In a certain survey, 500people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 52% said "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security. Complete parts (a) through (d) below. a. Are any of the three requirements violated? Can a test about a population proportion using the normal approximation method be used? A.The conditions np≥5 and...

Subjects