First defective on the second draw

Question

A tray holds 4 defective parts and 6 good parts, 10 in total. You test parts one at a time, without replacement.

What is the probability that the first defective part appears on exactly the second draw?

Accepted Answer

"First defective on the second draw" means the first part is good and the second is defective. Two draws, chained. Draw 1 good. 6 good out of 10: \frac{6}{10}. Draw 2 defective. After one good leaves, all 4 defectives remain out of 9: \frac{4}{9}. Multiply: \frac{6}{10}	imes\frac{4}{9}=\frac{24}{90}=\frac{4}{15}\approx 0.267. Takeaway. A short wait is just a short chain: one good draw, then the first defective. Update the counts between the two draws and multiply.

First defective on the second draw

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