Question

Two bad oranges are accidentally mixed with ten good ones. Three oranges are drawn at random without replacement from this lot. Obtain the probability distribution for the number of bad oranges,

Answer 1

All oranges are good $={\left(\frac{8}{10}\right)}^3$

$=\frac{64}{125}$

Two oranges are bad $=\frac{2}{10}\times \frac{2}{10}\times \frac{8}{10}$

$=\frac{4}{125}$

One orange bad $=\frac{2}{10}\times \frac{8}{10}\times \frac{8}{10}$

$=\frac{16}{125}$

All oranges bad $={\left(\frac{2}{10}\right)}^3$

$=\frac{1}{125}$

Hence, solved.