19 (12 points) Whether a company invests in a project is decided by three decision-makers, A, B, and C. Each of them has one "agree," one "neutral," and one "disagree" vote. When voting, each person must and can only cast one vote, and the probability of each person casting any one of the three types of votes is $\frac{1}{3}$. Their votes do not influence each other. The rule is: if the voting result includes at least two "agree" votes, the company will decide to invest in the project; otherwise, the company will abandon the investment.
(1) Find the probability that the company decides to invest in the project;
(2) Find the probability that the company abandons the investment and the voting result includes at most one "neutral" vote.
19 （1）The probability that the company decides to invest in the project is
$$
P=\mathrm{C}_{3}^{2}\left(\frac{1}{3}\right)^{2}\left(\frac{2}{3}\right)+\mathrm{C}_{3}^{3}\left(\frac{1}{3}\right)^{3}=\frac{7}{27} .
$$
（2）The company decides to abandon the investment in the project and the voting results have at most one "neutral" vote, with the following four scenarios:
\begin{tabular}{|c|c|c|c|}
\hline & Number of "agree" votes & Number of "neutral" votes & Number of "disagree" votes \\
\hline Event $A$ & 0 & 0 & 3 \\
\hline Event $B$ & 1 & 0 & 2 \\
\hline Event $C$ & 1 & 1 & 1 \\
\hline Event $D$ & 0 & 1 & 2 \\
\hline
\end{tabular}
$$
\begin{array}{c}
P(A)=\mathrm{C}_{3}^{3}\left(\frac{1}{3}\right)^{3}=\frac{1}{27}, \\
P(B)=\mathrm{C}_{3}^{1}\left(\frac{1}{3}\right)^{3}=\frac{3}{27}, \\
P(C)=\mathrm{C}_{3}^{1} \mathrm{C}_{2}^{1}\left(\frac{1}{3}\right)^{3}=\frac{6}{27}, \\
P(D)=\mathrm{C}_{3}^{1}\left(\frac{1}{3}\right)^{3}=\frac{3}{27} .
\end{array}
$$

Since $A$, $B$, $C$, and $D$ are mutually exclusive, we have
$$
P(A+B+C+D)=P(A)+P(B)+P(C)+P(D)=\frac{13}{27} .
$$