In 10 balls, 3 are defective. If 2 are chosen at random, find variance (σ^2) of the defective balls.

Question

In 10 balls, 3 are defective. If 2 are chosen at random, find variance \((\sigma ^ 2)\) of the defective balls.

Answer 1

Answer is: \(\frac{28}{75}\) 

\(= \left(\frac{3}{5}\right)^2.\frac{7}{15} + \left(\frac{2}{5}\right)^2 . \frac{7}{15} +\left(\frac{7}{5}\right)^2 . \frac{1}{15}\)  

\(= \frac{63+28+49}{375} = \frac{140}{375} = \frac{28}{75}\)