Question

A box of 10 items, 2 are defective. Items are randomly selected from the box one by one and examined. What is the probability that the sixth item selected is the last defective

Answer 1

The sixth item selected is the last defective if among the first five items there is one defective.

The corresponding probability is

$\frac{8}{{10}} \cdot \frac{7}{9} \cdot \frac{6}{8} \cdot \frac{5}{7} \cdot \frac{2}{6} \cdot 5 = \frac{5}{9}$

Since 5 parts remain, including one defective, the wanted probability is

$\frac{5}{9} \cdot \frac{1}{5} = \frac{1}{9}$

Answer: $\frac{1}{9}$