First part defective, is the next one defective too?

Question

A box holds 10 parts, of which 3 are defective and 7 are good. An inspector pulls two parts one after another without replacement. The first part is defective. Given that, what is the probability the second part is also defective?

Accepted Answer

Once one defective part is removed and kept aside, the box contains: - 10 - 1 = 9 parts total, - 3 - 1 = 2 defective parts. The next draw is equally likely among the remaining parts, so: P(	ext{second defective} \mid 	ext{first defective}) = \frac{2}{9} \approx 0.222. Finding one defect uses up part of the small defective pool, so the chance of a second defect falls from 3/10 to 2/9. Takeaway. In small batches, each removal noticeably shifts the odds; update the defective count and the total together before computing the next probability.

First part defective, is the next one defective too?

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