1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Annette [7]
3 years ago
10

The computers of nine engineers at a certain company are to be replaced. Four of the engineers have selected laptops and the oth

er 5 have selected desktops. Suppose that four computers are randomly selected. (a) How many different ways are there to select four of the nine computers to be set up?
(b) What is the probability that exactly three of the selected computers are desktops?

(c) What is the probability that at least three desktops are selected?
Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
4 0

Answer:

a) There are 126 different ways are there to select four of the nine computers to be set up.

b) 31.75% probability that exactly three of the selected computers are desktops.

c) 35.71% probability that at least three desktops are selected.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, there are no replacements. Which means that after one of the 9 computers is selected, there will be 8 computers.

Also, the order that the computers are selected is not important. For example, desktop A and desktop B is the same outcome as desktop B and desktop A.

These are the two reasons why the combinations formula is important to solve this problem.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

(a) How many different ways are there to select four of the nine computers to be set up?

Four computers are selected from a set of 9.

So

T = C_{9,4} = \frac{9!}{4!(9-4)!} = 126

There are 126 different ways are there to select four of the nine computers to be set up.

(b) What is the probability that exactly three of the selected computers are desktops?

Desired outcomes:

3 desktops, from a set of 5

One laptop, from a set of 4.

So

D = C_{5,3}*C_{4,1} = 40

Total outcomes:

From a), 126

Probability:

P = \frac{40}{126} = 0.3175

31.75% probability that exactly three of the selected computers are desktops.

(c) What is the probability that at least three desktops are selected?

Three or four

Three:

P = \frac{40}{126}

Four:

Desired outcomes:

4 desktops, from a set of 5

Zero laptop, from a set of 4.

D = C_{5,4}*C_{4,0} = 5

P = \frac{5}{126}

Total(three or four) probability:

P = \frac{40}{126} + \frac{5}{126} = \frac{45}{126} = 0.3571

35.71% probability that at least three desktops are selected.

You might be interested in
Which of the following is the conjugate of a complex number with 2 as the real part and −8 as the imaginary part?
vampirchik [111]
The complex number is given as: 2-8i

So for conjugate, you just flip the sign of the imaginary part:

2+8i will be the answer
3 0
3 years ago
Read 2 more answers
Beth will borrow 10,000 which earns 4% compound interest and she will repay that amount in 20 years. How much interest was earne
gtnhenbr [62]

Answer: 18,000

Step-by-step explanation: 10,000 borrowed + the 4% earned x the amount paid within 20 years

5 0
3 years ago
Read 2 more answers
Please help me with this question!!
quester [9]

Answer:

Step-by-step explanation:

a1 = 6

a2 = 10

a3 = 14

The next member of the sequence is 4 more than the current sequence. Therefore d = 4

a1 = 6

d = 4

n = 13

an = a1 + (n - 1)*d

an = 6 + (n - 1)*4

a_13 = 6 + 12*4

a_13 = 6 + 48

a_13 = 54

8 0
2 years ago
Can someone please help me I posted this multiple times but no one answers pls help me quick​
mario62 [17]
You would have to make 465=1550-7 1/2 x and find x
Subtract 1550 from both sides
-1085=-7 1/2x
Divide -7 1/2 on both sides
And the answer is 144 2/3
Sorry about ur bad luck
6 0
2 years ago
What is the volume of a rectangular prism with side lengths of x, x +4, and 2x-1
marysya [2.9K]

kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

6 0
3 years ago
Other questions:
  • Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If
    12·1 answer
  • Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that s
    12·1 answer
  • You are studying for your final exam of the semester. up to this point,you recieved 3 exam scores of 76%,99%, and 86%. to reciev
    13·2 answers
  • The scatter plot below shows the ages and heights of a varsity basketball team. Each dot represents one player. What is the tota
    9·2 answers
  • What is the area of a triangle with a base of 7 mm and a height of 10 mm
    14·1 answer
  • Simplify the expression -3.7 + 5g + 4k + 11.1 + (-10g)
    11·1 answer
  • Help as soon as possible
    7·1 answer
  • Please help mee!!!<br><br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B6%7D%7B-2%7D%3D-1" id="TexFormula1" title="\frac{x+6}
    14·2 answers
  • Please answer 5-10 and get brainliest
    6·2 answers
  • I need help again lol its meee
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!