Question

**Three factories F1, F2 and F3 respectively produce 25%,
35% and 40% of the total number of electrical parts intended for
the assembly of a machine. These factories respectively produce 1%,
2% and 3% of defective parts.**

We notice : The event A : "the part is produced by the F1
factory"

The event B : "the part is produced by the F2
factory"

The event C : "the part is produced by the F3 factory"

The event D : "the part is defective".

A) What is the probability that a randomly selected part will be defective?

B) Suppose you take a random part and it's defective. Calculate the probability that this part will be produced by the F2 factory.

Answer #1

P(A): Probability part is produced by the F1 factory = 0.25

P(B): Probability part is produced by the F2 factory = 0.35

P(C): Probability part is produced by the F3 factory = 0.4

P(D|A): Probability that part is defective given that it is from F1 factory = 0.01

P(D|B): Probability that part is defective given that it is from F2 factory = 0.02

P(D|C): Probability that part is defective given that it is from F3 factory = 0.03

a) P(D): Probability part is defective (Using Bayes Thorem) = P(A)*P(D|A) + P(B)*P(D|B) + P(C)*P(D|C)

= 0.25*0.01 + 0.35*0.02 + 0.4*0.03

= 0.0025+0.007+0.012

= 0.0215

b) P(B|D): Probability that part is produced from F2 factory given that it is defective = (P(B)*P(D|B))/P(D)

= (0.35*0.02)/0.0215

= 0.007/0.0215

= 0.326

Two machines each produce batches of part Q7BC. A random sample
of Q7BC parts from each machine’s recent production produced the
following frequency table. One Q7BC part is selected randomly.
Frequencies
Machine A
Machine B
Totals
Defective (D)
5
2
7
Not Defective (N)
145
48
193
Totals
150
50
200
Express each desired probability using
proper probability notation. Then find the probability using our
probability framework. Show your work.
Find the probability that the part was produced by machine...

Total
Defective (D)
Good (G)
110
40
70
Line 1 (1)
105
25
80
Line 2 (2)
215
65
150
Tota
A manufacturer is testing the production of a new
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and each part is inspected for defects. The results are summarized
in the table below:
1) Find the probability the part is defective
,P(D)
2) Find the probability the part is produced on Line
1,P(L2)
3)Find the probability...

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In the autumn of 2007, Alaska Airlines executives adjourned at
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