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
Andreyy89
3 years ago
15

g Suppose a factory production line uses 3 machines, A, B, and C for making bolts. The total output from the line is distributed

as follows: A produces 25%, B produces 35%, and C produces 40%. The defect rate for A is 5%, B is 4%, and C is 2%. If a bolt chosen at random is found to be defective, what is the probability that it came from machine A
Mathematics
1 answer:
Vladimir [108]3 years ago
3 0

Answer:

The probability that it came from A, given that is defective is 0.362.

Step-by-step explanation:

Define the events:

A: The element comes from A.

B: The element comes from B.

C: The element comes from C.

D: The elemens is defective.

We are given that P(A) = 0.25, P(B) = 0.35, P(C) = 0.4. Recall that since the element comes from only one of the machines, if an element is defective, it comes either from A, B or C. Using the probability axioms, we can calculate that

P(D) = P(A\cap D) + P(B\cap D) + P(C\cap D)

Recall that given events E,F the conditional probability of E given F is defined as

P(E|F) = \frac{P(E\cap F)}{P(F)}, from where we deduce that

P(E\cap F) = P(E|F)P(F).

We are given that given that the element is from A, the probability of being defective is 5%. That is P(D|A) =0.05. Using the previous analysis we get that

P(D) = P(A)P(D|A)+P(B) P(D|B) + P(C)P(D|C) = 0.05\cdot 0.25+0.04\cdot 0.35+0.02\cdot 0.4 = 0.0345

We are told to calculate P(A|D), then using the formulas we have

P(A|D) = \frac{P(A\cap D)}{P(D)}= \frac{P(D|A)P(A)}{P(D)}= \frac{0.05\cdot 0.25}{0.0345}= 0.36231884

You might be interested in
Help ASAPpppppppppp plsssssss and ty
jok3333 [9.3K]
DONT CLCIK THE LINK PLEASE REPORT IT
5 0
2 years ago
June served 4/9 of 18 liters of fruit punch. How many liters does she have left?
victus00 [196]
She has 10 liters left.  Find 4/9 of 18 by multiplying 4/9 and 18.  4/9 of 18 is 8, so she served 8 of the 18, leaving 10 liters.
3 0
3 years ago
Read 2 more answers
What is the value of 8 to the 4th power
Alex73 [517]

Answer:

8 x 8 x 8 x 8 = 4096

Step-by-step explanation:

Its an exponent which means you multiply 8 by itself 4 times to get 4096.

5 0
3 years ago
What is the answer to:<br> -4(2x+2) &lt;-40
mars1129 [50]

Answer: x > 6

Step-by-step explanation:  -4(2x+2) < -40

-8x - 8 < -40

      +8     +8

-8x < 48

/-8x   /-8x

x  > 6              *The less than sign got flipped to a greater than sign because we divided by a negative.

5 0
2 years ago
How can you determine if a number is a rational number
Murljashka [212]
Rational numbers can be written as a fraction
7 0
3 years ago
Other questions:
  • What multiplies to 10 and adds to 8
    13·2 answers
  • Molly is wrapping up parts of sandwiches to sell at her sandwich cart. She cuts each sandwich into fourths and then wraps each f
    14·1 answer
  • The first three steps for solving the quadratic equation by completing the square are shown. Fill in the missing number in the l
    11·2 answers
  • Dylan has $14.00 to spend at the book fair. He decides to buy two paperbacks for $4.50 each. Then, he sees some sticker books. A
    10·1 answer
  • DEF rotates 90 degrees clockwise about point A to create D’E’F. Therefore, which equation must be true
    8·1 answer
  • I REALLY NEED HELP PLS!!! Devon earned $42,500 last year and spent 12% of it on home repairs. How much did he spend on his home?
    9·1 answer
  • Need help ASAP!! Tyyy
    5·1 answer
  • A water container is 1/8 full. 35 litres if water are now poured into the container. The container is now 1/4 full.
    7·1 answer
  • At an auto repair shop. 3.5 hours of labour costs $311.50. What is the labour
    13·2 answers
  • Calculate the amount of dextrose in 756 mL D10W
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!