A machine produces $0$, $1$ or $2$ defective pieces in a day with associated probability of $1/6$, $2/3$ and $1/6$, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

1. $1$ and $1/3$
2. $1/3$ and $1$
3. $1$ and $4/3$
4. $1/3$ and $4/3$