Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

3 bad apples, 15 good apples.
Let X be no of bad apples
Then $\mathrm{P}(\mathrm{X}=0)=\frac{{}^{15}\mathrm{C}_2}{{}^{18}\mathrm{C}_2}=\frac{105}{153}$

$\mathrm{P}(\mathrm{X}=1)=\frac{{}^3\mathrm{C}_1\times {}^{15}\mathrm{C}_1}{{}^{18}\mathrm{C}_2}=\frac{45}{153}$

$\mathrm{P}(\mathrm{X}=2)=\frac{{}^3\mathrm{C}_2}{{}^{18}\mathrm{C}_2}=\frac{3}{153}$

$\mathrm{E}\left(\mathrm{X}\right)=0\times \frac{105}{153}+1\times \frac{45}{153}+2\times \frac{3}{153}=\frac{51}{153}$

$=\frac{1}{3}$

$Var\left(\mathrm{X}\right)=\mathrm{E}\left({\mathrm{X}}^2\right)-\left(\mathrm{E}\right(\mathrm{X}){)}^2$

$=0\times \frac{105}{153}+1\times \frac{45}{153}+4\times \frac{3}{153}-{\left(\frac{1}{3}\right)}^2$

$=\frac{57}{153}-\frac{1}{9}=\frac{40}{153}$