On an avenue there are 10 traffic lights. Due to a system failure, the traffic lights were without control for one hour, and fixed their lights only in green or red. The traffic lights operate independently; the probability of showing green is $\frac{2}{3}$ and of showing red is $\frac{1}{3}$. A person walked the entire avenue during the period of the failure, observing the color of the light of each of these traffic lights. What is the probability that this person observed exactly one signal in green? (A) $\frac{10 \times 2}{3^{10}}$ (B) $\frac{10 \times 2^{9}}{3^{10}}$ (C) $\frac{2^{10}}{3^{100}}$ (D) $\frac{2^{90}}{3^{100}}$ (E) $\frac{2}{3^{10}}$
On an avenue there are 10 traffic lights. Due to a system failure, the traffic lights were without control for one hour, and fixed their lights only in green or red. The traffic lights operate independently; the probability of showing green is $\frac{2}{3}$ and of showing red is $\frac{1}{3}$. A person walked the entire avenue during the period of the failure, observing the color of the light of each of these traffic lights.\\
What is the probability that this person observed exactly one signal in green?\\
(A) $\frac{10 \times 2}{3^{10}}$\\
(B) $\frac{10 \times 2^{9}}{3^{10}}$\\
(C) $\frac{2^{10}}{3^{100}}$\\
(D) $\frac{2^{90}}{3^{100}}$\\
(E) $\frac{2}{3^{10}}$