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
34kurt
3 years ago
14

A machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%). Prior to shipm

ent produced parts are passed through an automatic inspection machine, which is supposed to be able to detect any part that is obviously defective and discard it. However, the inspection machine is not perfect. A part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input. Slightly defective parts are marked as defective and discarded 40% of the time, and obviously defective parts are correctly identified and discarded 98% of the time.
Required:
a. What is the total probability that a part is marked as defective and discarded by the automatic inspection machine?
b. What is the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped?
c. What is the probability that a part is 'bad' (obviously defective) given that it makes it through the inspection machine and gets shipped?
Mathematics
1 answer:
AURORKA [14]3 years ago
5 0

Answer:

(a) 0.0686

(b) 0.9984

(c) 0.0016

Step-by-step explanation:

Given that a machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%).

Let A, B, and C be the events of defect-free, slightly defective, and the defective parts produced by the machine.

So, from the given data:

P(A)=0.90, P(B)=0.03, and P(C)=0.07.

Let E be the event that the part is disregarded by the inspection machine.

As a part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input.

So, P\left(\frac{E}{A}\right)=0.02

Now, from the conditional probability,

P\left(\frac{E}{A}\right)=\frac{P(E\cap A)}{P(A)}

\Rightarrow P(E\cap A)=P\left(\frac{E}{A}\right)\times P(A)

\Rightarrow P(E\cap A)=0.02\times 0.90=0.018\cdots(i)

This is the probability of disregarding the defect-free parts by inspection machine.

Similarly,

P\left(\frac{E}{A}\right)=0.40

and \Rightarrow P(E\cap B)=0.40\times 0.03=0.012\cdots(ii)

This is the probability of disregarding the partially defective parts by inspection machine.

P\left(\frac{E}{A}\right)=0.98

and \Rightarrow P(E\cap C)=0.98\times 0.07=0.0686\cdots(iii)

This is the probability of disregarding the defective parts by inspection machine.

(a) The total probability that a part is marked as defective and discarded by the automatic inspection machine

=P(E\cap C)

= 0.0686 [from equation (iii)]

(b) The total probability that the parts produced get disregarded by the inspection machine,

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

\Rightarrow P(E)=0.018+0.012+0.0686

\Rightarrow P(E)=0.0986

So, the total probability that the part produced get shipped

=1-P(E)=1-0.0986=0.9014

The probability that the part is good (either defect free or slightly defective)

=\left(P(A)-P(E\cap A)\right)+\left(P(B)-P(E\cap B)\right)

=(0.9-0.018)+(0.03-0.012)

=0.9

So, the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped

=\frac{\text{Probabilily that shipped part is 'good'}}{\text{Probability of total shipped parts}}

=\frac{0.9}{0.9014}

=0.9984

(c) The probability that the 'bad' (defective} parts get shipped

=1- the probability that the 'good' parts get shipped

=1-0.9984

=0.0016

You might be interested in
Will give Brainliest!! Please answer these 5 Algebra questions about if it is an Association or Causation really easy. - Thank y
babunello [35]
6 is association

7 is association

8 is association

9 is association

10 is association
5 0
2 years ago
Tyler's brother works in a shoe store.
Alina [70]
The amount he would make per hour is $12.60
4 0
1 year ago
sketch and label the sampling distribution for the sample proportion of games containing a "big bang", according to the Central
Daniel [21]

Answer:  D

Step-by-step explanation:

Sketch and label the sampling distribution for the sample proportion of games containing a big bang, according to the Central Limit Theorem, assuming that the grandfather's null hypothesis is true. Also check whether or not the conditions hold for the CLT to apply. Of the 95 games in our sample, 47 contained a big bang.

8 0
3 years ago
Solve (2x+3) ( x-7)=0​
Rus_ich [418]

Answer:

Step-by-step explanation:

Either,

2x+3=0

2x=-3

x=-3/2

Or,

( x-7)=0​

x=7

If you found my answer useful then please mark me brainliest.

5 0
2 years ago
Read 2 more answers
Instructions: State what additional information is required in order
irga5000 [103]

Answer:

TU ≅ CB

Step-by-step explanation:

HL Postulates that when a leg and the hypotenuse of a right triangle are congruent to a corresponding leg and hypotenuse of another, then both right triangles are congruent.

Both right triangles shown in the diagram above is indicated to possess corresponding lengths of a leg, that is side UV ≅ side BA

We need an additional information that shows that the hypotenuse, TU, of ∆TUV is congruent to the hypotenuse, CB of ∆CBA.

Therefore, additional information needed is TU ≅ CB

8 0
3 years ago
Other questions:
  • Pedro cut a sheet of poster board into 10 equal parts. His brother used some of the poster board and now 8/10 is left. Pedro wan
    8·2 answers
  • One of two supplementary angles is with 30° larger than the other. Find the angles.
    7·1 answer
  • A river is flowing at the speed of 2 miles per hour. A kayaker moves 528 feet upstream in 20 minutes. At this rate, how fast wou
    12·1 answer
  • Find the distance of 2 cities that are 2 inches apart on a scale of 1/4inch=50miles
    15·1 answer
  • Simplify: <br><br> I'm going to send you the picture lol, wait a minute...
    8·1 answer
  • How much more will 22,000 earn in interest than 14000 if both are invested in savings accounts with apys of 5.4% for a year?
    7·2 answers
  • Solve the equation 2 + x/-10 = 2/5
    14·2 answers
  • There are 18 football teams in a league,
    11·1 answer
  • 5. Simplify the expression and find its value when p= 4 and q = -5:
    11·2 answers
  • Simplify this expression<br> 6x -8y -5x + 3y
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!