For each of the five questions in this exercise, only one of the four proposed answers is correct.\\
The candidate will indicate on his/her work the number of the question and the chosen answer.\\
No justification is required.\\
A wrong answer, multiple answers, or the absence of an answer to a question neither gives nor removes points.

An urn contains 15 indistinguishable balls to the touch, numbered from 1 to 15.\\
The ball numbered 1 is red.\\
The balls numbered 2 to 5 are blue.\\
The other balls are green.\\
We choose a ball at random from the urn.\\
We denote $R$ (respectively $B$ and $V$) the event: ``The ball drawn is red'' (respectively blue and green).

\textbf{Question 1:}\\
What is the probability that the ball drawn is blue or numbered with an even number?

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
$\frac { 7 } { 15 }$ & $\frac { 9 } { 15 }$ & $\frac { 11 } { 10 }$ & None of the previous statements is correct. \\
\hline
\end{tabular}
\end{center}

\textbf{Question 2:}\\
Given that the ball drawn is green, what is the probability that it is numbered 7?

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
$\frac { 1 } { 15 }$ & $\frac { 7 } { 15 }$ & $\frac { 1 } { 10 }$ & None of the previous statements is correct. \\
\hline
\end{tabular}
\end{center}

A game is set up. To be able to play, the player pays the sum of 10 euros called the stake. This game consists of drawing a ball at random from the urn.
\begin{itemize}
  \item If the ball drawn is blue, the player wins, in euros, three times the number of the ball.
  \item If the ball drawn is green, the player wins, in euros, the number of the ball.
  \item If the ball drawn is red, the player wins nothing.
\end{itemize}
We denote $G$ the random variable that gives the algebraic gain of the player, that is, the difference between what he wins and his initial stake.\\
For example, if the player draws the blue ball numbered 3, then his algebraic gain is $-1$ euro.

\textbf{Question 3:}\\
What is the value of $P ( G = 5 )$ ?

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
$\frac { 1 } { 15 }$ & $\frac { 2 } { 15 }$ & $\frac { 1 } { 3 }$ & None of the previous statements is correct. \\
\hline
\end{tabular}
\end{center}

\textbf{Question 4:}\\
What is the value of $P _ { R } ( G = 0 )$ ?

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
0 & $\frac { 1 } { 15 }$ & 1 & None of the previous statements is correct. \\
\hline
\end{tabular}
\end{center}

\textbf{Question 5:}\\
What is the value of $P _ { ( G = - 4 ) } ( V )$ ?

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Answer A & Answer B & Answer C & Answer D \\
$\frac { 1 } { 15 }$ & $\frac { 4 } { 15 }$ & $\frac { 1 } { 2 }$ & None of the previous statements is correct. \\
\hline
\end{tabular}
\end{center}