This exercise is a multiple choice questionnaire.\\
For each question, only one of the four proposed answers is correct.\\
No justification is required.\\
A wrong answer, multiple answers or the absence of an answer to a question neither awards nor deducts points.\\
The five questions are independent.\\
A production line produces mechanical parts. It is estimated that $4 \%$ of the parts produced by this line are defective.\\
We randomly choose $n$ parts produced by the production line.\\
The number of parts produced is large enough that this choice can be treated as a draw with replacement.\\
We denote $X$ the random variable equal to the number of defective parts drawn.\\
In the following three questions, we take $n = 50$.

\begin{enumerate}
  \item What is the probability, rounded to the nearest thousandth, of drawing at least one defective part?\\
a. 1\\
b. 0,870\\
c. 0,600\\
d. 0,599
  \item The probability $p ( 3 < X \leqslant 7 )$ is equal to :\\
a. $p ( X \leqslant 7 ) - p ( X > 3 )$\\
b. $p ( X \leqslant 7 ) - p ( X \leqslant 3 )$\\
c. $p ( X < 7 ) - p ( X > 3 )$\\
d. $p ( X < 7 ) - p ( X \geqslant 3 )$
  \item What is the smallest natural integer $k$ such that the probability of drawing at most $k$ defective parts is greater than or equal to $95 \%$ ?\\
a. 2\\
b. 3\\
c. 4\\
d. 5
\end{enumerate}

In the following questions, $n$ no longer necessarily equals 50.\\
4. What is the probability of drawing only defective parts?\\
a. $0,04 ^ { n }$\\
b. $0,96 ^ { n }$\\
c. $1 - 0,04 ^ { n }$\\
d. $1 - 0,96 ^ { n }$\\
5. Consider the Python function below. What does it return?

\begin{verbatim}
def seuil (x) :
    n=1
    while 1-0.96**n <x :
        n = n + l
    return n
\end{verbatim}

a. The smallest number $n$ such that the probability of drawing at least one defective part is greater than or equal to x .\\
b. The smallest number $n$ such that the probability of drawing no defective parts is greater than or equal to x.\\
c. The largest number $n$ such that the probability of drawing only defective parts is greater than or equal to x.\\
d. The largest number $n$ such that the probability of drawing no defective parts is greater than or equal to x.