Here is the distribution of the main blood groups of the inhabitants of France. $A+, O+, B+, A-, O-, AB+, B-$ and $AB-$ are the different blood groups combined with the Rh factor.

A random experiment consists of choosing a person at random from the French population and determining their blood group and Rh factor.

We adopt notations of the type:
$A+$ is the event ``the person has blood group A and Rh factor $+$''
$A-$ is the event ``the person has blood group A and Rh factor $-$''
$A$ is the event ``the person has blood group A''

Parts 1 and 2 are independent.

\textbf{Part 1}

We denote $Rh+$ the event ``The person has positive Rh factor''.

\begin{enumerate}
  \item Justify that the probability that the chosen person has positive Rh factor is equal to 0.849.
  \item Demonstrate using the data from the problem statement that $P_{Rh_+}(A) = 0.450$ to 0.001 near.
  \item A person remembers that their blood group is AB but has forgotten their Rh factor. What is the probability that their Rh factor is negative? Round the result to 0.001 near.
\end{enumerate}

\textbf{Part 2}

In this part, results will be rounded to 0.001 near.

A universal blood donor is a person with blood group O and negative Rh factor. Recall that $6.5\%$ of the French population has blood group $O-$.

\begin{enumerate}
  \item We consider 50 people chosen at random from the French population and we denote $X$ the random variable that counts the number of universal donors.\\
  a. Determine the probability that 8 people are universal donors. Justify your answer.\\
  b. Consider the function below named \texttt{proba} with argument \texttt{k} written in Python language.
\begin{verbatim}
def proba(k) :
    p = 0
    for i in range(k+1) :
        p = p + binomiale(i,50,0.065)
    return p
\end{verbatim}
  This function uses the binomial function with arguments $i, n$ and $p$, created for this purpose, which returns the value of the probability $P(X=i)$ in the case where $X$ follows a binomial distribution with parameters $n$ and $p$.\\
  Determine the numerical value returned by the \texttt{proba} function when you enter \texttt{proba(8)} in the Python console. Interpret this result in the context of the exercise.
  \item What is the minimum number of people to choose at random from the French population so that the probability that at least one of the chosen people is a universal donor is greater than 0.999.
\end{enumerate}