• Support PF! Buy your school textbooks, materials and every day products Here!

Probability of defective machines question

  • Thread starter zhfs
  • Start date
  • #1
10
0
[solved]probability question

Homework Statement



Three machines A, B, and C produce 50%, 30% and 20% respectively of the total
number of items at a factory. Each produces a number of defective: 3%, 4% and 5%
respectively.
(a) If an item produced by one of these machines is selected, find the probability that
it is defective.
(b) Now suppose that a manufactured item is selected at random and is found to be
defective. Find the probability that this item was produced by machine A.

Homework Equations



N/A

The Attempt at a Solution



is part (a)
Pr = (3%+4%+5%)/(50%*30%*20%)?

and no idea on part b

thanks a lot!
 
Last edited:

Answers and Replies

  • #2
Use Bayes' theorem.

Let D be the event that a selected item is defective

Let A, B, and C be the events that that an item is produced by machine A, B, and C respectively

[tex] P(D) = P(D\cap A) + P(D \cap B) +P(D \cap C) [/tex]

[tex] = P(D|A)P(A) + P(D|B)P(B) + P(D|C)P(C) [/tex]

[tex] P(A|D) = \frac {P(A \cap D)}{P(D)}[/tex]

[tex] = \frac {P(D|A)P(A)}{P(D|A)P(A) + P(D|B)P(B) + P(D|C)P(C)} [/tex]
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,792
920
How I would do it: Imagine that 1000 of the items are produced. Then 50% of 1000= 500 come from machine A, 30% of 1000= 300 from machine B, and 20% of 1000= 200 from machine C.

Of the 500 from machine A, 3% of 500= 15 are defective, 4% of 300= 12 are from machine B, and 2% of 200= 4 are from machine C.

A total of 15+ 12+ 4= 41 defective items are produced of a total of 1000 items. With that information (a) is easy.

Of a total of 41 defective items, 15 of them were from A. With that information, (b) is easy.
 
  • #4
10
0
thank you guys!!
 

Related Threads for: Probability of defective machines question

Replies
6
Views
3K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
1K
Replies
6
Views
2K
Replies
1
Views
4K
Replies
5
Views
2K
Replies
2
Views
1K
  • Last Post
Replies
4
Views
899
Top