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
Alla [95]
3 years ago
12

In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacem

ent. Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements.
a. What is the probability that exactly one tank in the sample contains high-viscosity material?
b. What is the probability that at least one tank in the sample contains high-viscosity material?
c. In addition to the six tanks with high viscosity levels, four different tanks contain material with high impurities. What is the probability that exactly one tank in the sample contains high-viscosity material and exactly one tank in the sample contains material with high impurities?
Mathematics
1 answer:
Damm [24]3 years ago
5 0

Answer:

a) P(A) = 0,4607     or   P(A) = 46,07 %

b) P(B) = 0,7120   or 71,2 %

c) P(C) = 0,2055  or P(C) = 20,55 %

Step-by-step explanation:

We will use two concepts in solving this problem.

1.- The probability of an event (A) is for definition:

P(A) = Number of favorable events/ Total number of events FE/TE

2.- If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

a) The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )!    ⇒  C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!  

C ( 24,4) = 24*23*22*21/4*3*2

C ( 24,4) = 24*23*22*21/4*3*2    ⇒  C ( 24,4) =  10626

TE = 10626

Splitting the group of tanks in two 6 with h-v  and 24-6 (18) without h-v

we get that total number of favorable events is the product of:

FE = 6* C ( 18, 3)  = 6 * 18! / 3!*15!  =  18*17*16*15!/15!

FE =  4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0,4607     or   P(A) = 46,07 %

b) P(B) will be the probability of at least 1 tank contains h-v

P(B) = 1 - P ( no one tank with h-v)

Again Total number of events is 10626

The total number of favorable events for the ocurrence of P is C (18,4)

FE = C (18,4) = 18! / 14!*4! = 18*17*16*15*14!/14!*4!

FE = 18*17*16*15/4*3*2  = 3060

Then P = 3060/10626

P = 0,2879

And the probability we are looking for is

P(B) = 1 - 0,2879

P(B) = 0,7120   or 71,2 %

c) We call P(C) the probability of finding exactly 1 tank with h-v and t-i

having 4 with t-i tanks is:

reasoning the same way but now having 4 with t-i (impurities) number of favorable events is:

FE = 6*4* C(14,2) = 24 * 14!/12!*2!

FE = 24* 14*13*12! / 12!*2

FE = 24*14*13/2    ⇒  FE = 2184

And again as the TE = 10626

P(C) = 2184/ 10626

P(C) = 0,2055  or P(C) = 20,55 %

You might be interested in
Write each sentence as an equation.
Montano1993 [528]

Answer:

  1. <em> n - 2 = 52</em>
  2. <em>x - 3 = 12</em>
  3. <em>5 + x = 50 - 10</em>
  4. <em>3 + x = 60</em>
  5. <em>x + 6 = 10 - 2</em>
  6. <em>x - 9 = 12</em>
  7. <em>x + 5 = 13</em>
  8. <em>x + 10 = 20</em>
  9. <em>5x = 25</em>
  10. <em>2x = 5 + 2</em>

<em />

please rate and heart :)

have a great day!!

3 0
3 years ago
Is Brainly most scanning for anyone else right now? And how do I fix it I have deadlines coming up
Studentka2010 [4]

Answer:

what-

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
PLEASE HELP FAST! What is the distance between the two points located at (14, 27) and (14, −8)? this is in units.
KIM [24]

Answer:

13

Step-by-step explanation:

13

3 0
2 years ago
Read 2 more answers
THIS IS VERY IMPORTANT I WILL GIVE BRAINLIEST TO THE PERSON WHO DOES ALL 4 QUESTIONS FOR ME.
devlian [24]

Answer:

6. 130/130.5

7. C, 14 pink roses and 26 red roses

8. A, 18 model cars and 27 model airplanes

9. $359.10

Step-by-step explanation:

Number 6 involves two potential answers because although 30% of 435 is 130.5 you cannot have half of a person at a baseball game.

6 0
2 years ago
For the data set below, which of the following measures is greatest? (20, 25, 30, 31, 32, 45, 45, 80). I will give 28 points!
shutvik [7]

Answer:

D.Mean

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • String A is three times the length of String B. Sarah cut String
    7·1 answer
  • 4 times a number cubed decreased by 7... write an algebraic expression
    9·1 answer
  • 4 x 3 =<br> Known fact: 2 X 3 =<br> Double the product: 6 + 6 =
    14·1 answer
  • List the numbers from greatest to least.
    10·1 answer
  • Find the leg (in inches) of the triangle whose hypotenuse is 10 inches and whose other leg is 3.25 inches. Round to the nearest
    13·1 answer
  • F(x)=8−4x−x^3 <br> g(x)=x^2+7x−9 <br> Find f(x)+g(x).
    8·1 answer
  • Holly bought 23 tickets to the baseball game. She got a group rate that gave her $4 off of the regular ticket price for each tic
    7·2 answers
  • Susan’s ribbon is 3.8 metres long. <br> What is the length of her ribbon in millimetres?
    7·1 answer
  • 10 points for whoever can solve this for my brother
    9·2 answers
  • Enter the unknown number that makes the equation true. 75 + 3 x ☐ = 372
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!