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A company has 4 production sections, viz. S1, S2, S3 and S4 [#permalink]
04 Nov 2004, 17:41

A company has 4 production sections, viz. S1, S2, S3 and S4 which contribute 30%, 20%, 28% and 22% respectively to the total output. It was observed that these sections respectively produced 1%, 2%, 3% and 4% defective units. If a unit is selected at random and found to be defective, what is the probability that the unit so selected came from section S1.

Let us take 100 units , so S1 produces 30 S2 produces 20 S3 produces 28 S4 produces 22

No of defective from S1 = 1% = .3 No of defective from S2 = 2% = .2 No of defective from S3 = 3% = .28 No of defective from S4 = 4% = .22

Total defective = 1

so, prob of defective, piece = 1/100

P(A+B) = P(A/B)*P(B)

30/100 * .3/30 = P(A/B) * 1/100

or P(A/B) = .3

= 30%

I may be misunderstanding this question but portion in red should be:
No of defective from S2 = 2% = .4
No of defective from S3 = 3% = .84
No of defective from S4 = 4% = .88
Should it not?
Total would then be .3+.4+.84+.88 = 2.42
.3/2.42=12.4% _________________

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