For each of the five questions in this exercise, only one of the four proposed answers is correct. No justification is required. A wrong answer, a multiple answer or the absence of an answer to a question neither awards nor deducts points.

We consider L a list of numbers consisting of consecutive terms of an arithmetic sequence with first term 7 and common difference 3, the last number in the list is 2023, namely:
$$\mathrm{L} = [7, 10, \ldots, 2023].$$

\textbf{Question 1:} The number of terms in this list is:
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
2023 & 673 & 672 & 2016 \\
\hline
\end{tabular}
\end{center}

\textbf{Question 2:} We choose a number at random from this list. The probability of drawing an even number is:
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
$\frac{1}{2}$ & $\frac{34}{673}$ & $\frac{336}{673}$ & $\frac{337}{673}$ \\
\hline
\end{tabular}
\end{center}

We choose a number at random from this list. We are interested in the following events:
\begin{itemize}
  \item Event $A$: ``obtain a multiple of 4''
  \item Event $B$: ``obtain a number whose units digit is 6''
\end{itemize}
We are given $p(A \cap B) = \frac{34}{673}$.

\textbf{Question 3:} The probability of obtaining a multiple of 4 having 6 as the units digit is:
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
$\frac{168}{673} \times \frac{34}{673}$ & $\frac{34}{673}$ & $\frac{17}{84}$ & $\frac{168}{34}$ \\
\hline
\end{tabular}
\end{center}

\textbf{Question 4:} $P_B(A)$ is equal to:
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
$\frac{36}{168}$ & $\frac{1}{2}$ & $\frac{33}{168}$ & $\frac{34}{67}$ \\
\hline
\end{tabular}
\end{center}

\textbf{Question 5:} We choose, at random, successively, 10 elements from this list. An element can be chosen multiple times. The probability that none of these 10 numbers is a multiple of 4 is:
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
\begin{tabular}{ c }
Answer A \\
$\left(\frac{505}{673}\right)^{10}$ \\
\end{tabular} & \begin{tabular}{ c }
Answer B \\
$1 - \left(\frac{505}{673}\right)^{10}$ \\
\end{tabular} & \begin{tabular}{ c }
Answer C \\
$\left(\frac{168}{673}\right)^{10}$ \\
\end{tabular} & \begin{tabular}{ c }
Answer D \\
$1 - \left(\frac{168}{673}\right)^{10}$ \\
\end{tabular} \\
\hline
\end{tabular}
\end{center}