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
Iteru [2.4K]
2 years ago
14

In a widget factory, machines A, B, and C manufacture, respectively, 20, 30, and 50 percent of the total. Of their output 6, 3,

and 2 percent are defective widgets. A widget is drawn at random from the produce and is found defective. What are the probabilities that it was manufactured by machines A, B, and C?
Mathematics
1 answer:
steposvetlana [31]2 years ago
6 0

Answer:

38.71% probability it was manufactured by machine A.

29.03% probability it was manufactured by machine B.

32.26% probability it was manufactured by machine C.

Step-by-step explanation:

We have these following probabilities:

A 20% probability that the chip was fabricated by machine A.

A 30% probability that the chip was fabricated by machine B.

A 50% probability that the chip was fabricated by machine C.

A 6% probability that a chip fabricated by machine A was defective.

A 3% probability that a chip fabricated by machine B was defective.

A 2% probability that a chip fabricated by machine C was defective.

The question can be formulated as:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

P = \frac{P(B).P(A/B)}{P(A)}

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

What are the probabilities that it was manufactured by machines A, B, and C?

Machine A

What is the probability that the widget was manufactures by machine A, given that it is defective?

P(B) is the probability that it was manufactures by machine A. So P(B) = 0.20

P(A/B) is the probability that a widget is defective, given that it is manufactured by machine A. So P(A/B) = 0.06

P(A) is the probability that a widget is defective. This is the sum of 6% of 20%, 3% of 30% and 2% of 50%. So

P(A) = 0.06*0.20 + 0.03*0.30 + 0.02*0.5 = 0.031

So

P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.2*0.06}{0.031} = 0.3871

38.71% probability it was manufactured by machine A.

Machine B

What is the probability that the widget was manufactures by machine B, given that it is defective?

P(B) is the probability that it was manufactures by machine B. So P(B) = 0.30

P(A/B) is the probability that a widget is defective, given that it is manufactured by machine B. So P(A/B) = 0.03

P(A) = 0.06*0.20 + 0.03*0.30 + 0.02*0.5 = 0.031

So

P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.3*0.03}{0.031} = 0.2903

29.03% probability it was manufactured by machine B.

Machine C

What is the probability that the widget was manufactures by machine C, given that it is defective?

P(B) is the probability that it was manufactures by machine C. So P(B) = 0.50

P(A/B) is the probability that a widget is defective, given that it is manufactured by machine C. So P(A/B) = 0.02

P(A) = 0.06*0.20 + 0.03*0.30 + 0.02*0.5 = 0.031

So

P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.5*0.02}{0.031} = 0.3226

32.26% probability it was manufactured by machine C.

You might be interested in
What is the volume of a spherical shell with inner radius 7 and outer radius 8?
yuradex [85]

Answer:

707.9 cm³

Step-by-step explanation:

What is the volume of a spherical shell with inner radius 7 and outer radius 8?

The formula for the volume of a sphere is given as;

= 4/3 × π × r³

From the above question:

inner radius 7 and outer radius 8

Hence, the volume of a sphere with

inner radius 7 and outer radius 8 is calculated as:

V = (4/3 × π × 8³ ) - (4/3 × π × 7³)

V = 4/3 × π ×(8³- 7³)

V = 4/3 × π × (512 - 343)

V = 4/3 × π × 169

V = 707.9055446 cm³

V = 707.9 cm³

6 0
3 years ago
Please look at the box
jenyasd209 [6]

Answer:

m = slope

(x_1, y_1) = coordinates of first point in the line

(x_2, y_2) = coordinates of second point in the line

6 0
2 years ago
Read 2 more answers
Company A is offering $6,000 for the first month's salary and will increase the amount each month by $5,000. Company B is offeri
Alex17521 [72]

The month in which Company B's payment will first exceed Company A's payment is C) Month 7.

Step-by-step explanation:

Step 1:

Company A offers $6,000 for the first month and increases the salary each month by $5,000.

Company B offers $700 for the first month but doubles the payments each month.

We need to determine which month company B's payment is greater than company A's payment.

Step 2:

According to the table, at month 6 company A pays $31,000 while company B pays $22,400.

However after this month, in the seventh-month company A pays $36,000 while company B pays $44,800, which is higher than company A's salary.

So The month in which Company B's payment will first exceed Company A's payment is C) Month 7.

4 0
3 years ago
Can you guys help me finish this quiz tonight
ira [324]

The Answer Is g(x)=1/3x^2

Use (3,3) to find the equation.

3^2x1/3=3

Meaning y or g(x) equals 3. Which is true.

5 0
3 years ago
Read 2 more answers
Rational numbers word problem please help
eimsori [14]

4000/100= 40

40x6= 240

240x1.5= 360

360/4= $90 per person

7 0
3 years ago
Other questions:
  • 100 points
    14·2 answers
  • I WILL MARK BRAINLIEST IF CORRECT!
    6·2 answers
  • Toms baseball team wins 5 out of every 12 games they play if team player 36how many games Tom wins
    9·2 answers
  • If a beam can hold 2,000 pounds at 15 feet, what is the safe load if the length of the beam is 10 feet?
    14·2 answers
  • To wrap a gift, you can choose from 4 kinds of wrapping paper, 6 gift bags, 2 colors of ribbon, 5 bows, and 2 stickers. You choo
    5·2 answers
  • Find the sum or type "impossible"<br><br>2 -5<br> +<br>3 6<br>​
    8·1 answer
  • A school has all of the students in grade 8 take a math test. Several samples are taken from the results. Which of the following
    9·1 answer
  • Which area is closest to the area of Utah?
    13·1 answer
  • Find the value of the triangle shown below <br> X=
    10·1 answer
  • Brainliest points whatever you want please
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!