To conduct a survey, an employee interviews people chosen at random in a shopping mall. He wonders whether at least three people will agree to answer.

\begin{enumerate}
  \item In this question, we assume that the probability that a person chosen at random agrees to answer is 0.1. The employee interviews 50 people independently. We consider the events:\\
  $A$: ``at least one person agrees to answer''\\
  $B$: ``fewer than three people agree to answer''\\
  $C$: ``three or more people agree to answer''.\\
  Calculate the probabilities of events $A$, $B$ and $C$. Round to the nearest thousandth.
  \item Let $n$ be a natural integer greater than or equal to 3. In this question, we assume that the random variable $X$ which, to any group of $n$ people interviewed independently, associates the number of people who agreed to answer, follows the probability distribution defined by:
$$\left\{\begin{array}{l}\text{For every integer } k \text{ such that } 0 \leqslant k \leqslant n-1,\; P(X = k) = \frac{\mathrm{e}^{-a} a^k}{k!}\\\text{and } P(X = n) = 1 - \sum_{k=0}^{n-1} P(X=k)\end{array}\right.$$
\end{enumerate}