3. A fair dice is thrown three times. The results of the first, second and third throw are recorded as $x, y$ and $z$, respectively. Suppose $x+y=z$. What is the probability that at least one of $x, y$ and $z$ is 2 ?
(A) $\frac{1}{12}$;
(B) $\frac{3}{8}$;
(C) $\frac{8}{15}$;
(D) $\frac{1}{3}$;
(E) $\frac{7}{13}$.
3. Answer: (C).
If $z=2$, then $(x, y)=(1,1)$.
If $z=3$, then $(x, y)=(1,2),(2,1)$.
If $z=4$, then $(x, y)=(1,3),(2,2),(3,1)$.
If $z=5$, then $(x, y)=(1,4),(2,3),(3,2),(4,1)$.
If $z=6$, then $(x, y)=(1,5),(2,4),(3,3),(4,2),(5,1)$.
Out if these 15 cases, 8 of them contain at least one 2 . Hence, the required probability is $\frac{8}{15}$.