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

18 apples total (3 rotten, 15 good). X = number of rotten in draw of 2.

$$P(X=0)=\frac{\binom{15}{2}}{\binom{18}{2}}=\frac{105}{153}$$. $$P(X=1)=\frac{\binom{3}{1}\binom{15}{1}}{\binom{18}{2}}=\frac{45}{153}$$. $$P(X=2)=\frac{\binom{3}{2}}{\binom{18}{2}}=\frac{3}{153}$$.

$$E(X)=0+45/153+6/153=51/153=1/3$$. $$E(X^2)=0+45/153+12/153=57/153$$.

$$Var=E(X^2)-[E(X)]^2=\frac{57}{153}-\frac{1}{9}=\frac{57}{153}-\frac{17}{153}=\frac{40}{153}$$.

The answer is Option (4): $$\frac{40}{153}$$.