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
A home improvement store sold wind chimes for $30 each.A costumer signed up for a free membership card and recieved a 5% discoun
Anton [14]
29.925 is the correct answer
8 0
3 years ago
Read 2 more answers
! PLEASE HELP! Will mark BRAINILEST find F(-4) !
Darya [45]
F(-4)= 9*3^(-4)=9/(3^4)=1/9
3 0
3 years ago
NEED HELP A family traveling home after a reunion Records the time in hours and the distance they are from home in miles based o
Marysya12 [62]

Answer:

200 miles

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Compare the two expressions using , or =. 100 x 8 ______ 25 x (4 x 9)
VikaD [51]

Answer:

, ig

Step-by-step explanation:

4 0
3 years ago
Can you please help me with this question ​
patriot [66]
7 guests
It costs 5 dollars per guest, so divide 35 by 5
3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the Volume of the shape below?
    14·1 answer
  • A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker
    10·1 answer
  • If the midpoint of segment AB is M(1,-3) and B(5,-10), find the coordinates of point A.
    15·1 answer
  • Anyone know 4 equivalent fractions to 5/8,4/3,5/7 and 8/9? For 37 points plsss help
    7·1 answer
  • You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over. You want to divide
    15·2 answers
  • Tom's red bicycle travels 50 ft for every 3 pedal turns. How many pedal turns are needed to travel a mile (5,280 ft) ?
    15·1 answer
  • Paul's Pizzeria sells 45 cheese pizzas in 20 pepperoni pizzas each week what is the ratio of cheese pizzas to pepperoni pizzas s
    15·2 answers
  • At what point does the line with equation y=4-2x cut the y axis?
    12·1 answer
  • Help on number 12 pls
    6·1 answer
  • Find the volume <br><br> A. 150 cm3<br><br> B. 180 cm3<br><br> C. 90 cm3<br><br> D. 90 cm2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!