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
Crazy boy [7]
3 years ago
14

A component is assembled in a four-step process. The probability of making a defect in step 1 is 10%; in step 2, 20%; in step 3,

8%; and in step 4, 5%. What is the probability that the component will be defective?
Mathematics
2 answers:
rjkz [21]3 years ago
4 0

Answer:

0.37072

Step-by-step explanation:

Let A be the event that step 1 is defective (P(A) = 10%), B the event that step 2 is defective(P(B) = 20%), C the event that step 3 is defective (P(C) = 8%), D the event that step 4 is defective(P(D) = 5%). Let us suppose that the occurance of a failure at any step is indepent of the other steps.

Recall the following properties

P(A) = 1- P(A^c)

(A\cup B )^c = A^c \cap B^c)

And given A, B, C, D independent , then

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

REcall that if the a set of events A,B,C,D are independent, their complements are also indepent.

Since we are asked for the probability of a defective item, this means that at least one of the steps is defective. Then, we are asked for the following probability:

P(A\cup B \cup C \cup D) = 1 - P((A\cup B \cup C \cup D)^c) = 1 - P(A^c \cap B^c \cap C^c \cap D^c ) = 1 - P(A^c)P(B^c) P(C^c) P(D^c) = 1-(1-P(A))(1-P(B))(1-P(C))(1-P(D))

= 1-(0.9)(0.8)(0.92)(0.95) = 0.37072

PilotLPTM [1.2K]3 years ago
4 0

Answer:

Correct answer is 37.1 % . Explanation is given below :

Production                                                                    

steps deffective   without defects  (100)            (100-100=0)

1          10                      90   100*90/100=90         100-90=10

2          20                       80   90*80/100=72                100-72=28

3          8                       92   72*92/100=66.24     100-66.24-33.76

4          5                      95     66.24*95/100=62.928       100-62.928=37.1

You might be interested in
Solve for x. 5/3 times x ≤ 10
arlik [135]
The answer is x <span> ≤ 6, i think</span>
5 0
3 years ago
Read 2 more answers
What are the factors of 3
k0ka [10]
3 and 1 are the factors of 3 duhhh lol
4 0
2 years ago
Read 2 more answers
A football team loses 3 yards on one play and 6 yards on another play. Write a sum of negative integers to represent this situat
stepan [7]
-3 + (-6) = -9
This relates to to the problem because the team has lost a total of nine yards.
4 0
2 years ago
What is the value of t in the equation 3(2t + 5) = 5t + 25?
11Alexandr11 [23.1K]
<span>3(2t + 5) = 5t + 25
6t + 15 = 5t + 25
6t - 5t = 25 - 15
t = 10</span>
8 0
3 years ago
12/39 in simplest form is 4/13 what are two ways to get there
arlik [135]
Divide 3 on the numerator and denominator.

Hoped this helped.

~Bob Ross®
7 0
2 years ago
Read 2 more answers
Other questions:
  • A behavioral scientist investigated whether there is a significant difference in the percentages of men and women who purchase s
    14·1 answer
  • Trinity created a game that uses a card number 1 to 8 and a six sided cube numbered 1 to 6. Each player chooses one card and roa
    7·1 answer
  • Please help meeee “which of the following represents a relation and not a function”
    10·1 answer
  • I need help on this question
    9·2 answers
  • Identify as either rational or irrational, and approximate to the tenths place.
    8·1 answer
  • What is the value of y in the triangle?
    7·1 answer
  • 900 is ___ the value of 9
    5·1 answer
  • I NEED HELP now pls pls
    9·2 answers
  • (02.02)A shape is shown on the graph:
    7·1 answer
  • Using principle of mathematical induction prove that 6^-1 divisble by 5 .​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!