Question 71
Alberto, Barbara and Carlo are playing cards. At each hand, the winner gains 2 points, while the other two players lose one point each. Initially, everyone has 0 points. What is the probability that, after 10 hands, everyone is again at zero points?
(A) 0
(B) $\frac{1}{5}$
(C) $\frac{1}{3}$
(D) $\frac{\binom{10}{6}}{3^{10}}$
(E) $1-\left(\frac{2}{3}\right)^{10}$.
(A) 0
(B) $\frac{1}{5}$
(C) $\frac{1}{3}$
(D) $\frac{\binom{10}{6}}{3^{10}}$
(E) $1-\left(\frac{2}{3}\right)^{10}$.